Game Theory (Part 4) - The Median Voter Theorem

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This post is part of my course on game theory. For an index, see here. The course follows the lectures by Ben Polak which are available on the Open Yale Courses website.

In the previous post we discussed the iterated deletion of dominated strategies and the concept of common knowledge. In this post, we will continue to explore these two issues by looking at an easy, but famous theorem from political science: the Median Voter Theorem.


1. The Set Up
There are two candidates running for president. Each candidate must position themselves along the ideological left-right axis in order to appeal to voters. Suppose there are ten possible ideological locations along this axis. Suppose further that voters are evenly distributed along this axis, i.e. approx. 10% of the pool of voters are located at each of the ten ideological positions. See the following diagram.

This election can be modelled as a game. The candidates are the players; the strategies are the positions they can choose along the ideological spectrum; and the payoffs are the percentages of the vote they manage to capture. Obviously the goal of each player is to maximise their share of the vote.

To help them decide what their strategy should be we need first to introduce a couple of rules about the voting patterns of the electorate. Suppose that voters always prefer the candidate that is closest to their own ideological position. This means that an extreme right wing voter will vote for a left wing candidate provided that candidate is less left wing than their rival. In addition, suppose that if the two candidates are an equal distance from the voter’s preferred position, the vote will be split evenly between the two candidates. In other words, one candidate will get 5% of the available 10%, and the other candidate will get the remaining 5%.

For some reason, as I write this down, it sounds very complicated. But it’s really not.


2. Iterated Deletion of Dominated Strategies
Now that we have the set up for the game, we can proceed to solve it for both candidates. To do this, we will once again make use of the iterated deletion of dominated strategies. Remember, this involves putting yourself (if you are a player) in the shoes of your opponent and thinking about how they would respond to your choices.

Let’s start with candidate A and see what would happen to him if he decided to position himself at location number 1 (i.e. he chooses the extreme left wing position).

It’s pretty clear that this would be a silly thing to do. Why? Because location 2 dominates location 1: it yields a higher payoff no matter what candidate B does. To see this, work out the expected payoff for A of location 2 compared to location 1, against all possible strategies of candidate B. We’ll go through some of the relevant calculations here. An obvious pattern will emerge after a few, thereby rendering the rest of the calculation unnecessary:

Assuming B plays location 1 

• Ua (1, 1) → A gets 50% of the vote, B gets 50% of the vote 
• Ua (2, 1) → A gets 90% of the vote, B gets 10% of the vote

Assuming B plays location 2 

• Ua (1, 2) → A gets 10% of the vote, B gets 90% of the vote 
• Ua (2, 2) → A gets 50% of the vote, B gets 50% of the vote

Assuming B plays location 3 

• Ua (1, 3) → A gets 15% of the vote, B gets 85% of the vote 
• Ua (2, 3) → A gets 20% of the vote, B gets 80% of the vote

Assuming B plays location 4 

• Ua (1, 4) → A gets 20% of the vote, B gets 80% of the vote 
• Ua (2, 4) → A gets 25% of the vote, B gets 75% of the vote

We could continue on through all ten locations, but its pretty clear by now that no matter what B does, A is always better off playing location 2 instead of location 1. Thus, 1 can be considered a dominated strategy.

Since 1 is dominated, we should eliminate it from the pool of viable strategies. What happens then? Location 2 becomes dominated by location 3. In other words, A will find that it’s always better to choose location 3, irrespective of what his opponent does. Thus, 2 should also be removed from the pool of viable choices. I leave the proof of this to the reader.

It is important to note that 3 only becomes a dominant strategy after 1 has been removed from the pool of viable strategies.

The reasoning that underlies the deletion of 1 and 2 works from the opposite side as well, i.e. for locations 10 and 9. What’s more, the reasoning works until all strategies apart from 5 and 6 are eliminated for both candidates.

This is the prediction of the median voter theorem: both candidates end up positioning themselves in the middle of the ideological spectrum.

3. Problems with the Model
Although the Median Voter Theorem is sometimes thought to work well in predicting the behaviour of U.S. presidential candidates, there are certain key weaknesses in the model.

First, the model assumes that voting preferences are arrayed along a single dimension. It could be argued in response that political preferences are in fact multidimensional. Strangely, although I think political preferences should be multidimensional, I find, in practice, there is much to be said for the idea that people align themselves along a simple, single left-right dimension.

Second, the model assumes that preferences are equally distributed along the spectrum when in reality they might be skewed towards one end or the other. Actually, it turns out that this isn’t that big of a problem. It just means that candidates will/should position themselves in the middle of whatever the actual distribution is.

Third, the model assumes that candidates can simply pick the ideological position that suits their needs. In reality, candidates come with histories (voting records, policy statements etc.) that might make it difficult for such positioning to be credible to the electorate.

Finally, the model assumes that every voter actually votes. If not-voting is an option, things become more complicated. The model also becomes more complicated when there are more than two candidates running for election.

Griffiths and Wilkins on Evolutionary Debunking Arguments (Part Two)

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Would anyone trust in the convictions of a monkey's mind?

(Part One)

This post is the second in a brief series on the paper "When do Evolutionary Explanations of Belief Debunk Belief?" by Paul Griffiths and John Wilkins (GW - again, apologies for the abbreviation). In this paper, GW argue that it is possible to respond to evolutionary debunking arguments (of the sort covered here) by constructing a Milvian Bridge, i.e. showing how truth-tracking can be complementary to evolutionary success.

In the previous entry, I outlined the basic elements of GW's argument. The last thing I discussed was their claim that our commonsense beliefs are not debunked by evolutionary explanations. In other words, their claim that a Milvian Bridge can be constructed to cover commonsense beliefs. The key question now is how much further can the Milvian Bridge be extended. GW argue that it can be extended to cover scientific beliefs, but not ethical or religious beliefs.

Although I agree with GW about scientific and ethical beliefs, I am not entirely convinced by their support for the evolutionary debunking of religious beliefs. My contention is that the argument they offer in defence of scientific beliefs could easily be co-opted by the defender of religious beliefs. Whether I am right in this depends heavily on whether I am correct in my interpretation of the argument they offer in support of scientific beliefs, so I turn to that first.

(Note: I am not going to cover GW's discussion of ethical beliefs since I have covered that topic at length before)


1. From Commonsense to Science 
As noted last time, although we can be reasonably confident that our cognitive mechanisms do not fundamentally mislead us about the nature of the objects and entities with which we interact on a daily basis, the kinds of beliefs we have about such objects have no ultimate ontological significance. This is in stark contrast to scientific beliefs about the nature of such objects and entities (and more besides) which, while maybe not representative of the ultimate truth, are thought to get us a good deal closer to the ultimate level.

How can these scientific beliefs be justified? Surely, even if the proponent of the evolutionary debunking argument accepted GW's point about commonsense beliefs, they could still maintain that scientific beliefs are debunked. Scientific beliefs, they will say, take us beyond the realm of commonsense, and while it may be true that our cognitive mechanisms have evolved to track the truth within the realm of commonsense, this gives us no ground for thinking that those same cognitive mechanisms can extend us beyond that realm.

GW offer two points that count against the debunker's arguments in this regard. The first seems slightly weak, and I don't think GW mean for it to count for much, but I'll mention it anyway. It is that scientific beliefs, unlike the kinds of commonsense or intuitive beliefs that may have some evolutionary salience, are not the product of one organism's innate cognitive mechanisms. Scientific beliefs are cognitive innovations, built upon the shoulders of giants, and spread by cultural diffusion.

I take it that while the possibility of cognitive innovations being spread through cultural diffusion has some significance, it doesn't really count against the debunker's arguments. Why not? Because there are many beliefs spread by cultural diffusion but that might be thought to lack the status of knowledge. Indeed, religious beliefs may be a classic example of this.

GW's second point is rather more interesting and significant. It is that we can be confident in the content of our scientific beliefs because they are arrived at via a method that is itself justified by commonsense standards. GW refer to this as an indirect, as opposed to a direct, Milvian Bridge. I think their argument has a certain amount of appeal. Speaking for myself, I can certainly say that when I first learned about double-blind testing it seemed like an obviously correct process for removing biased or distorted interpretations of experimental results.

Since I think this point has significant ramifications, I want to try to sketch out their reasoning in slightly more formal terms. I call this the "indirect Milvian Bridge argument":

• (1) Our commonsense beliefs are warranted due to the fact that they are produced by cognitive mechanisms that have evolved to track the truth within the commonsense realm (premise, from previous argumentation).

• (2) If a set of beliefs X is likely to be warranted, and a set of beliefs Y can be derived using standards set by X, then Y is also likely to be warranted (indirect Milvian bridge principle).

• (3) Scientific beliefs can be derived using standards set by commonsense beliefs.

• (4) Therefore, scientific beliefs are likely to be warranted.

I hope this is an accurate reflection of GW's argument. Note that the content of scientific beliefs need not be consistent with commonsense, all that matters is that the method used to derive those beliefs is consistent with commonsense. Indeed, scientific beliefs are quite often counter-intuitive.

2. Debunking Religious Beliefs

As noted in the intro, I'm going to skip over GW's discussion of ethical beliefs. One point worth noting is that GW endorse the view held by Street and Kahane that a possible response to evolutionary debunking arguments in ethics is to reject realist conceptions of ethical truth. This endorsement is significant because GW query at the end of their article whether a similar strategy might be available to the religious believer. But I'll leave this issue to the side in order to focus solely on their argument that religious beliefs are debunked by evolutionary explanations.

GW support this argument by reference to some of the leading theories on the evolutionary origin of religious beliefs. Broadly speaking, there are two main categories of such theories (i) those that maintain that religious beliefs confer some sort of evolutionary benefit; and (ii) those that maintain that religious beliefs are a by-product of other cognitive mechanisms that conferred some kind of evolutionary benefit. There might also be a third category that combines both of these approaches (i.e. first a by-product, then an adaptation).

An example of a theory belonging to the first category is that of David Sloan Wilson. He argues that religious belief was selected for due to its potential to enhance social cohesion and prosocial behaviour. Examples of theories belonging to the second category would be those of Barrett, Boyer and Atran. They argue, for instance, that belief in a divine agent is a by-product of a cognitive mechanism for detecting agency (sometimes called the "hyper-active agency detection device" or HADD).

GW argue that neither of these theories can be used to support the existence of a Milvian Bridge for religious belief. Why not? Because in neither case is there any suggestion that religious beliefs were the product of truth-tracking processes. In Wilson's case, the beliefs are selected for their social benefits, not for their ability to track the mind-independent truth. In the case of by-product theories, the beliefs are produced by a mechanism with a propensity for making type 1 (false positive) errors.

3. An Objection

Although I am certainly inclined towards their conclusion, I think GW's argument against religious beliefs is a little too quick. In particular, I worry about their dismissal of by-product theories. They seem to accept, too readily, that beliefs in the existence of a divine mind will be the result of a type 1 error by the relevant cognitive mechanism.

Given my earlier formulation of the indirect Milvian bridge argument, it will probably come as no surprise to learn that this forms the backbone of my objection. I'm inclined to ask: If we are allowed to build an indirect bridge from the realm of commonsense to the realm of science, then why can't we build a similar bridge from the realm of commonsense to the realm of the divine? Here's what I have in mind.

First, I presume our beliefs about the existence of other agents are not massively erroneous (i.e. that, even though the rate of type 1 errors might be high, our HADD still picks out real agents more often than not), I do so on the grounds that, following GW's earlier arguments, other agents are part of our commonsense realm and our beliefs in this realm are likely to be truth-tracking.

Given these presumptions, I think it is plausible that our method for identifying agents in the commonsense realm could (maybe using other criteria set by our commonsense beliefs) be used to derive beliefs about the existence of other minds, including the divine mind. To quote Griffiths and Wilkins talking about scientific beliefs:

"If evolution does not undermine our trust in our cognitive faculties, neither should it undermine our trust in our ability to use those faculties to debug themselves - to identify their own limitations, as in perceptual illusions or common errors in intuitive reasoning."

Quite so, but why assume that we can't debug the HADD and still arrive at a belief in the existence of a divine mind? 

I suspect there are two types of response that GW might make to this. 

First, they could argue that they already acknowledge this possibility since they accept (at the very end of their article) that debunking is not disproving and that other reasons could be adduced in support of religious belief. I think that's right, but then I'm forced to wonder why we need the kind of argument that GW offer in support of scientific beliefs. Surely the concern of the debunker in both cases is with the possibility of justifiably moving beyond the commonsense realm; and surely the response, in both cases, is that an indirect Milvian bridge can be built? 

Second, they could argue that the problem with the HADD is that it is, contrary to my presumption, massively erroneous. That might be true too, but then I can't see why this wouldn't undermine their argument in defence of our commonsense beliefs. Surely other agents are part of our commonsense realm, and surely our cognitive mechanisms would have evolved to track the truth about such entities?

Okay, that's all I have to say on this for now. Hopefully, John or Paul might pop-up in the comments and offer some critique of what I've said. 

[Addendum: I'd like to add that I just came across this paper which seems to address the religious belief issue at considerable length.]

Griffiths and Wilkins on Evolutionary Debunking Arguments (Part One)

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Would anyone trust the convictions of a monkey's mind?

Last week, I put up a series of posts on Guy Kahane's article "Evolutionary Debunking Arguments". In the comments to one of them, John Wilkins said he would be interested in my comments on a related paper that he wrote with Paul Griffiths entitled "When do Evolutionary Explanations of Belief Debunk Belief?". This post is the first in a two-part series that attempts to do exactly that.

Griffiths and Wilkins (GW - I trust you'll forgive the abbreviation) argue that evolutionary explanations do not debunk commonsense and scientific beliefs, but that they do debunk moral and religious beliefs. In this post I'll try to summarise the basic elements of their argument. In the next post, I'll look in more detail at their arguments relating to scientific and religious beliefs. If you're interested in the critical commentary, skip to part two.


1. Debunking Arguments and the Milvian Bridge
Following Kahane, GW accept that evolutionary debunking arguments have the following basic structure:

Causal Premise: S's belief that P is caused by the evolutionary process X

Epistemic Premise: The evolutionary process X does not track the truth of propositions like P.

Conclusion: Therefore, S's belief that P is not justified (warranted).

As GW point out, the easiest way to undermine a debunking argument of this sort it to attack the epistemic premise, i.e. to argue that the evolutionary process does track the truth with respect to the relevant class of propositions. They refer to this response, cleverly,  as constructing a Milvian Bridge.

The Battle of the Milvian Bridge

The name comes from the famous battle of the Milvian Bridge which is often pinpointed as the origin of the emperor Constantine's conversion to Christianity. The reference is relevant in that Constantine's success at the battle is often attributed to his belief in (the Christian) God's existence. Assuming this belief to be true, as traditionally was the case, the idea is that Constantine's pragmatic success can be linked to his true beliefs. Thus the idea promoted by GW is that sometimes evolutionary success can be linked to warranted belief by means of a Milvian bridge:

Milvian Bridge Principle: X facts are related to the evolutionary success of X beliefs in such a way that it is reasonable to accept and act on X beliefs produced by our evolved cognitive faculties.

GW think a Milvian bridge can be built for commonsense and scientific beliefs, but not for moral and religious beliefs.


2. Levels of Explanation
One of the reasons that evolutionary debunking arguments seem compelling is their reliance on the assumption that fitness-tracking and truth-tracking are alternative forms of explanation, not complementary forms. Thus it seems that a cognitive bias or heuristic can be accounted for in terms of its fitness-enhancing capabilities, this rules out or lessens the probability that it is truth-tracking.

This, GW argue, is a mistake: fitness-tracking and truth-tracking are not alternatives. A fitness-tracking explanation takes place at a different level from a truth-tracking explanation. When we ask "why was trait A (seemingly) selected over trait B?", we are asking a question at the most abstract level of evolutionary explanation: the population level. At this level, one determines fitness by looking at the heritability, frequencies and fitness functions of a particular trait.

The truth tracking explanation takes place at a lower and more specific level. It concerns how an organism actually interacts with its environment. To say that a cognitive mechanism tracks the truth is akin to saying that a pair of claws are efficient flesh tearing machines. There is no reason why a cognitive mechanism cannot be both truth-tracking and fitness-enhancing; just as there is no reason why a pair of claws cannot be both efficient flesh-tearers and fitness enhancers.

3. Trade Offs and Constraints
To say that cognitive mechanisms can be both truth-tracking and fitness enhancing is not to say that they actually will be truth-tracking. GW argue that cognitive mechanisms will only be truth-tracking within certain constraints. They give two examples of such constraints.

Cognition is clearly a costly enterprise. Estimates vary, but approximately 20% of the human body's oxygen consumption is taken up by the brain, despite accounting for only 2% of its mass. Because it is so costly, GW argue it is unreasonable to assume that cognition plays no role in shaping human behaviour. At the same time, it needs to be borne in mind that resources spent on cognition cannot be spent on, for example, tissue maintenance or gamete production.

If the opportunity cost involved in cognition is taken into account, then it might turn out that many of the biases and quirks in human cognition are less arbitrary than they first appear. Indeed, Gerd Gigerenzer and his colleagues have been arguing for years that many human biases and heuristics are best understood as reasonable accommodations between cost and accuracy. In other words, our evolved cognitive mechanisms can be seen to track truth with relative efficiency subject to various costs.

In addition to this, the ability of our evolved cognitive mechanisms to track truth may be limited by the fact that on some tasks involving decision-making under uncertainty it is impossible to avoid making some kinds of error. Abstractly, these tasks require the organism to produce appropriate behavioural responses to signals of uncertain meaning. In such a task there are two basic errors the organism can make: (i) a type 1 (false positive) error; and (ii) a type 2 (false negative) error.

Each of these errors comes with an associated type of risk. Suppose the signal in question is the colouring of certain types of food and the appropriate behavioural response is either to eat the food or discard it. The organism might assume that bright colours indicate poisonous foods. In this case, an organism that makes a large number of false positive errors will run the risk of discarding a large number of consumable foodstuffs. An organism that makes a large number of false negative errors will run the risk of being poisoned.

But, and here's the crucial point, because uncertainty is a part and parcel of the cognitive task, evolutionary processes will be unable to avoid making some kind of error: any reduction in the risk of type 1 errors will increase the risk of type 2 errors, and vice versa. So the best that evolution can do is to achieve the most reasonable balance between the types of error that the organism makes.

Once again, there can be truth-tracking, but only subject to constraints.


4. The Milvian Bridge for Commonsense Beliefs
So far, GW have presented three key claims: (i) that the easiest way to respond to an evolutionary debunking argument is to construct a Milvian bridge, i.e. show that true beliefs can be linked to pragmatic success; (ii) that fitness-enhancing and truth-tracking explanations are not alternatives to one another; and (iii) that our cognitive mechanisms can track truth subject to certain constraints.

What sorts of implications can be drawn from these three claims? The first implication, according to GW, is that our commonsense beliefs are overwhelming likely to have tracked the truth because understanding of the commonsense realm is highly likely to be linked to evolutionary success. Now we must be careful about this for two reasons. First, we need to understand what GW mean by "commonsense belief" and second, we need to understand their views on the ontological significance of a commonsense belief.

As regards meaning, GW say that a commonsense belief is an everyday belief that guides action. I take it they intend by this to refer to our beliefs about the mid-sized objects and entities that we interact with on an ongoing basis: our fellow humans, basic foodstuffs, our bodily limbs, rocks, trees, chairs, cars, cabbages, kings and so on.

As regards the ontological significance of our everyday beliefs, GW make an interesting and important observation: the conceptual realm that is created by our commonsense beliefs has no ultimate ontological significance. Indeed, there is a certain relativity or flexibility to such conceptual schemes.

Lorenz with Geese

One example they use to illustrate their point is drawn from the field of ethology (study of animal behaviour). The cite Konrad Lorenz's famous work on birds which suggests that birds do not perceive or conceive of their fellow birds as particular individuals in the way that we do.  Instead, they conceive of a set of stimulus features that mark something as the appropriate object of a suite of behaviours. In doing so, the birds make no essential mistake or error about the ontological reality of their fellow birds. There is nothing necessarily wrong about ours or the birds' conceptual schemes, they are both valid.

To say that our commonsense beliefs have no ultimate ontological significance is not to say that we lack the means to acquire knowledge of the more fundamental levels of ontology. That is what science allows us to do, but our confidence in our scientific beliefs can be derived from our confidence in our commonsense beliefs, as we shall see in part two.

Draper on God and Evil (Part Three)

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(Part One, Part Two)

This post is part of a brief series on Paul Draper’s Plantinga Lecture “God and Evil: A Philosophical Inquiry”. In previous entries, I set out the basic structure of Draper’s argument, summarised the analogy he uses to illustrate some of his key points, and considered his defence of the first premise of his argument. In this entry, I focus on Draper’s defence of premises (2), (3) and (4).


1. The Defence of Premise (2)
The second premise of Draper’s argument is:

• (2) With respect to the data of good and evil, naturalism is much more accurate than theism.

There’s nothing too surprising about Draper’s defence of this premise. Anyone who has read his classic 1989 article will be familiar with the basic contours of his thinking on this matter.

In his lecture, he defends the premise by telling a story about two alien scientists who come to earth: Natty, the naturalist, and Theo, the theist. As they investigate the world, these two aliens acquire more and more data about good and evil. As they do so, they will try to make predictions about what they will learn about the conscious beings (those capable of experiencing pain or harm) who inhabit the earth.

Draper argues that Natty will be far more successful in making predictions about these conscious beings, and the fates that befall them, than Theo. For instance, Natty will be able to infer that the fate of conscious beings will be similar to that of unconscious beings such as plants. Why? Because on Natty’s worldview there is no reason to think that conscious beings will be treated any differently from unconscious beings: both are subject to the same process of evolution. On Theo’s worldview there is some reason to think they will be treated differently since conscious beings are capable of being morally wronged. Similarly, Natty will be able to infer that pain and pleasure are likely to be largely fitness-tracking experiences (i.e. tied to evolutionary success). Theo will be unable to make that inference because he has reason to think pain and pleasure will have some sort of deeper moral significance.

Of course, Theo can respond to both of these examples by playing the skeptical theist (ST) card. He can claim that he doesn’t know of all the entailment relations that can hold between possible goods and evils and that it is possible that God has some sort of “beyond-our-ken” reasons for allowing what we observe.

There are two points to be made about this kind of response. First, it does nothing to undermine premise 2. Anyone who adopts the ST-response must tacitly admit that naturalism is more accurate with respect to the data on good and evil. Second, at best this kind of response can be used to protect the other epistemic and evidential advantages that theism might have from being undermined by the data on good and evil. The problem is that ST might not be very successful in doing this. Indeed, it may come with significant epistemic costs of its own. This would actually have the effect of strengthening premises (3) and (4) of Draper’s argument. (I have written about these problems extensively on this blog).

A theist could also appeal to a theodicy in response to the problem of evil. Draper does not explore this possibility in his lecture, but suggests (maybe jokingly) that he will in his forthcoming book.

To sum up, Draper seems to defend premise (2) of his argument in the following manner:

• (2.1) The naturalist can make better predictions with respect to fates of conscious and unconscious creatures.
• (2.2) The naturalist can make better predictions with respect to the biological function of pleasure and pain.

The skeptical theist can interject here:

• (2.3) God could have beyond-our-ken reasons for allowing the particular distribution of goods and evils that we see.

But this can be responded to as follows:

• (2.4) This still implies that naturalism is better confirmed by the actual data on good and evil.
• (2.5) Skeptical theism is a position that comes with significant epistemic costs.

All of which gives us the following addition to our original argument map.

2. Defending Premise 3 and 4
Premise (3) of Draper’s argument states the following:

• (3) With respect to other data, any overall advantage in accuracy that theism has over naturalism is relatively small.

As Draper notes in his lecture, this premise is crucial and yet incredibly difficult to defend (or, indeed, reject). It suggests that in order to properly evaluate the success (or failure) of the problem of evil we must be able to say that theism and naturalism are roughly equally probable with respect to other available data (or, better, any advantage that theism might have must be outweighed by the disadvantage is has with respect to the existence of evil).

It’s difficult to say anything more conclusive about that here.

Let’s move on then to premise (4), which states:

• (4) Any other epistemic advantage that theism has over naturalism is relatively small.

Draper notes that there are several interesting routes that an objection to this premise could take. Perhaps fittingly, he focuses in his lecture on the Plantinga-style objection. Plantinga argues that we have non-inferential knowledge of theism thanks to the presence in us of a special faculty called the sensus divinitatus. He also argues that the knowledge provided by this special faculty might function as a defeater to any inferential or evidence-based justifications of naturalism.

• (4.1) The non-inferential knowledge of theism provided by the sensus divinitatus defeats the evidential knowledge in favour of naturalism.

Draper offers four responses to this kind of argument. I’ll just list them here:

• (4.2) The weight that should be afforded to an argument depends on the epistemic position of the person hearing the argument. Since not everyone has non-inferential knowledge of God, not everyone has access to the Plantingan defeater. To those people, Draper’s argument will still be relevant.
• (4.3) It is not clear (contra Plantinga) that theism strongly entails the existence of a sensus divinitatus.
• (4.4) Conversely, if theism does entail the existence of a sensus divinitatus then it must do so strongly (i.e. everyone must have one). Since not everyone seems to have a sensus divinitatus (including some self-professed Christians), its existence is disconfirmed by the evidence.
• (4.5) Current cognitive science of religion supports the existence of a broad sensus actoris (or hyperactive agency detector) it does not support the existence of a specific sensus divinitatus.

Before adding these points to the argument map, I should note that Draper goes on to suggest that (4.5) might not be that strong an objection since monotheism seems to survive defeaters better than animism or polytheism.

3. Does the Conclusion follow?
This brings us nearly to the end of Draper’s lecture. There’s just one last piece of business to wrap up. As noted in part one, the conclusion of Draper’s argument is as follows:

• (5) Therefore, theism is very probably false.

This conclusion does not follow straightforwardly from the premises. Draper shows that there is some further argumentation needed to justify that conclusion. The reasoning is roughly:

If premises 1 - 4 are true, then it follows that naturalism is more probable than theism. But naturalism is just one of the ways in which theism can be false. Thus, the falsity of theism must be as least as probable as the truth of naturalism. But then it does follow that if naturalism is much more probable than theism, then theism is very probably false. Why? Because the falsity of theism must be at least as probable at the truth of naturalism, and maybe even more so.

Draper on God and Evil (Part Two)

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(Part One)

This post is part of a brief series on Paul Draper’s Plantinga Lecture “God and Evil: A Philosophical Inquiry”. Part one introduced us to the basic structure of Draper’s argument and the analogy he uses to illustrate that structure. In this part, we’ll start to consider Draper’s defence of the argument. As noted last time, the lecture is really only a preview of his forthcoming book and so does not offer anything like a full defence of the relevant points.

I’ll just look at his defence of the first premise in this post.


1. The Simplicity of Naturalism
The first premise of Draper’s argument is the following:

(1) Naturalism is much simpler than theism.

In the philosophy of science, simplicity is typically assumed to be an explanatory virtue. An explanation is generally thought to be better than a rival if it is simpler. For Draper (and, indeed, others such as Swinburne) simplicity seems to affect the prior probability (or intrinsic) probability of a hypothesis.

While that is all well and good, there is a problem. There are a number of different ways of conceiving of theoretical simplicity. Perhaps the most well-known states that simplicity is a function of the number of hypotheses or axioms that must be presupposed in order to accept an explanation. This can be reformulated to have specifically ontological pretensions by stating that it relates to the number of ontological entities that must be presupposed. Another example would be that of Richard Swinburne. He offers a definition according to which a hypothesis is simpler if it postulates infinite as opposed to finite quantities.

Draper is aware of the dispute in the literature and tries to skirt it by offering yet another approach to the topic (thereby, irony of ironies, adding to the complexity of simplicity). He maintains that one hypothesis is simpler than another if it meets two conditions (i) it is more modest than the other and (ii) it has greater internal consistency than the other.

He illustrates what he means by referring back to his original example of Poisson’s spot (see part one for details). He asks us to imagine that in addition to wave-ism and particle-ism, there is a third theory on the nature of light called “particle-ism plus”. This theory claims that there are light particles but that they are carried by waves.

The interesting thing is that particle-ism plus is consistent with the presence of Poisson’s spot. So there doesn’t seem to be any reason to prefer wave-ism over it, at least by reference to that particular datum. But there is reason to prefer wave-ism with respect to simplicity. Why?

Well, because P-plus is clearly less modest than either particle-ism or wave-ism. It makes more specific claims about the nature of the world than either of the other theories. It thereby increases the chance of error. Furthermore, it has less internal coherence than the other theories. It only manages to account for the datum of Poisson’s spot by making considerable moves away from particle-ism towards wave-ism.

Returning to Draper’s argument, his claim is that theism is much like P-plus. For starters, theism, like P-plus, is a more specific version of another theory (in this case supernaturalism). And because it is more specific, it displays less modesty than supernaturalism (or, indeed, naturalism). Furthermore, while the specific claim of theism (i.e. there is an omni-propertied personal being) is not actively inconsistent with supernaturalism, it is certainly not a natural entailment or product of that more general theory.

All of this suggests that Draper is offering something like the following argument in support of premise (1):

• (1.1) A hypothesis H is simpler than a hypothesis H* if it is (a) more modest than H* and (b) more internally coherent than H*.

• (1.2) Naturalism is more modest and displays more internal coherence than theism.

• (1) Therefore, Naturalism is much simpler than theism.

2. Some Comments
Before moving on to consider Draper’s defence of premise (2) I want to say a couple of quick words about his defence of premise (1).

First, I’m not entirely convinced that Draper’s account of simplicity is correct, or whether its good to add another account to the pile, but I can let that slide and try to assess it on it own merits.

Second, I’m not sure the analogy Draper tries to make stacks up here. My feeling is that P-plus is less probable because it seems to have been so obviously introduced as an ad hoc saviour for particle-ism. In other words, it looks like a revision of particle-ism that is less modest because it is adopted in the face of unwelcome facts. This doesn’t seem to me to be at all like theism, which does not (yet) suffer from such ad hocery. Theism may suffer from immodest ad hocery when it is revised in the face of unwelcome facts, but since simplicity has to do with a priori plausibility this consideration seems not to apply here.

Now my reaction might just be an accidental by-product of how Draper presents his case: he discusses the simplicity of P-plus after having already discussed Poisson’s spot, and discusses the simplicity of theism prior to considering the problem of evil. If I abstracted away this sequence, the simplicity point might hold up.

Third, there is something a little stretched about the analogy Draper tries to draw between incoherence/inconsistency in the case of P-plus and incoherence/inconsistency in the case of theism. While it seems obvious enough that P-plus is some sort of an uncomfortable alliance between wave-ism and particle-ism, it seems less obvious that there is an uncomfortable alliance going on in the case of theism and supernaturalism. If theists had to make some concessions to the priority of the physical in formulating their hypothesis then maybe the analogy would hold up.

Furthermore, in his discussion of this point it seems like Draper is only saying that theism is not directly entailed by naturalism, which seems to me to be no different from his observation that theism is immodest when compared to supernaturalism and theism.

Finally, it occurs to me (although this is irrelevant to Draper’s argument) that there might be more specific forms of naturalism that could suffer from immodesty and incoherence (indeed, the more sophisticated forms of naturalism probably do). This is something to be borne in mind. While a vague and general form of naturalism might do well vis-a-vis theism, a more specific form may not.

Anyway, that's enough for now. In the next part I'll look at Draper's defence of (2).

Draper on God and Evil (Part One)

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Paul Draper delivered the Plantinga lecture last October. The lecture was effectively a sneak preview of his forthcoming book the Evidential Problem of Evil (according to his webpage). The text of the lecture has been made available online and I wanted to go through it over the next few posts.

As with all of his work, Draper’s lecture is both thoughtful and thought-provoking. It is also, on the face of it, quite humorous in places. Of course, it’s difficult to say how these things go over in person as opposed to on the page, but I can certainly say that some of the philosophical in-jokes elicited a wry smile from me as I read them.

Anyway, down to business. Draper’s lecture is entitled “God and Evil: A Philosophical Inquiry”. Unsurprisingly, it presents a basic argument against theism by focusing on a particular datapoint relating to evil. To support this argument, heavy use is made of an analogy drawn from a classic scientific dispute over the nature of light.

In this first part, I’ll outline the analogy, I’ll present Draper’s basic argument, and address some of the terminology he uses.


1. Poisson’s Spot
The analogy brings us back to the early 19th Century and a debate about the nature of light. At the time, there were two dominant schools of thought on the issue. According to one of these schools, light was a wave (call the relevant theory “wave-ism”); according to the other school, light was a stream of particles (call the relevant theory “particle-ism”). Neither theory seemed to have a decisive advantage over the other with respect to the data at the time.

All that was about to change. In 1818, a young scientist named Fresnel submitted work on wave diffraction to the French Academy of Sciences as part of a competition. Diffraction is what happens to a wave when it encounters an obstacle. One of the judges in the competition, Poisson, realised that Fresnel’s work could be used to confirm particle-ism over wave-ism was true (Poisson was a believer in particle-ism).

Poisson deduced that if a light was shone at a circular disc, then, if the wave theory were true, one would expect to see a single spot of light in the middle of the shadow cast by the disc. If the wave theory was false (as Poisson thought) no such spot should be visible. As fate would have it, the experiment actually confirmed the existence of the spot. The experiment is illustrated below.

Without getting too embroiled in the details, there are three important points arising from this story. First, there are two competing theories that seem, relative to one set of data, roughly equally probable (wave-ism and particle-ism). Second, there is a particular datapoint that seems to confirm one theory over another (the presence of Poisson’s spot). And third, there is the apparently reasonable conclusion that, as a result, wave-ism is more likely to be true than particle-ism.


2. Draper’s Basic Argument
The three features just alluded to are crucial to understanding why Draper discusses the example. His argument against theism, although certainly more complex, turns on a very similar pattern of reasoning. Once again we have two theories (naturalism, theism) which are symmetrical with respect to one set of data; we have a particular datapoint (existence of evil) which seems to confirm naturalism over theism; and we have the seemingly reasonable conclusion that naturalism is therefore more likely to be true than theism.

There are also some differences between the two cases that come to the fore in Draper’s subsequent analysis. Two differences seem worthy of mention at the outset: (i) Draper claims that naturalism is simpler than theism and thus has higher a priori probability; and (ii) it’s much more difficult to assess the respective merits of theism and naturalism.

This leads Draper to formulate and defend the following argument:

• (1) Naturalism is much simpler than theism.

• (2) With respect to the data of good and evil, naturalism is much more accurate than theism.

• (3) With respect to other data, any overall advantage in accuracy that theism has over naturalism is relatively small.

• (4) Any other epistemic advantage that theism has over naturalism is relatively small.

• (5)Therefore, theism is very probably false.

This is illustrated below. As you can see, I’ve placed a gap between the premises and the conclusion. This is because, as Draper acknowledges at the end of his lecture, the inference is not as straightforward as you might think.

Obviously, to make this argument in any way compelling, Draper needs to support each of its premises. Unfortunately, he doesn’t do all the necessary work in his lecture, he saves that for his forthcoming book. But he does sketch defences for (1) and (2) and offer some comment on (3) and (4). We’ll go through these in the subsequent posts.


3. Naturalism vs. Theism
Before we do that, we need to clarify some of the terminology employed in the argument. As can be seen, Draper is comparing naturalism and theism. But what do these respective hypotheses mean? Draper begins to answer this by noting that concrete reality seems to consist of a private, mental, subjective world, and a public, objective, physical world. He then drafts the following breakdown:

Naturalism: The view that the public, objective, physical world has ontological priority over the private, mental, subjective world. In other words, the view that the mental can be explained in terms of the physical.

Supernaturalism: The view that the private, mental, subjective world has ontological priority over the public, objective, physical world. In other words, the view that the physical can be explained in terms of the mental. In practice, this means that the physical world was created or brought about in order to fulfill or satisfy the purposes of one or many mental entities.

Theism: A sub-type of supernaturalism according to which the physical world was brought into being by a single, omnipotent, omniscient, and omnibenevolent mental entity.

Note here that theism is defined as a specific type of supernaturalism that makes specific claims about the type of mental entity responsible for the creation of the physical world. This turns out to be significant later in Draper’s argument. It is probably worth asking at this stage whether there are more specific versions of naturalism too. Presumably there are (e.g. single-universe vs. multiverse theories). This might be significant as well.

Anyway, that’s it for now. In the next part, I’ll look at Draper’s defence of premise (1) and (2).

Darwin and Moral Realism: The Survival of the Iffiest

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I’ve covered Sharon Street’s evolutionary debunking argument of objective (mind-independent) moral reality before. I’ve also covered some responses to the argument, along with some more general reflections on arguments of this sort. I’d recommend reading some of those posts before tackling this one.

In this entry, I’ll be covering the following article:

Skarsaune, K.O. “Darwin and Moral Realism: Survival of the Iffiest” (2011) 152 Philosophical Studies 229

It’s a direct response to Street’s Darwinian dilemma. So a quick recap on her argument is our first port of call.


1. Street’s Darwinian Dilemma
Non-natural moral realists believe that moral properties (values, rights, wrongs etc) exist in some mind-independent realm. Further, these realists tend to believe that we acquire knowledge of this realm through the exercise of our intuitive evaluative judgments. In other words, our intuitive evaluative judgments are some how in tune with this mind independent realm.

Now we all know (irrespective of our metaethical proclivities) that most of our intuitive evaluative judgments are the products of a complex evolutionary history. That is to say, most of our intuitive judgments can be said to have come about due to their fitness enhancing abilities. So, for example, our belief that we have certain duties to protect our offspring, or our enthusiasm for reciprocal forms of altruism, can be explained in terms of fitness enhancement.

But this creates a problem for the defender of moral realism. It implies that our evolved judgments have somehow managed to coincide with the mind-independent moral truth.

The thoughts set out in the preceding paragraphs can be expressed as an evolutionary debunking argument:

(1) Causal Premise: Our intuitive evaluative judgments are the product of a complex evolutionary processes.

(2) Epistemic Premise: Evolutionary processes are fitness enhancing, they do not track the truth of mind-independent moral properties.

(3) Therefore, our intuitive evaluative judgments are unjustified.

Street thinks that in responding to this argument the realist is confronted with a dilemma. As with all dilemmas, there are two horns on which they can impale themselves:

First Horn: They can argue that there is a relation between evolutionary processes and the mind-independent moral truth (which seems implausible).

Second Horn: They can argue that there is no such relation, in which case they land themselves in an unwelcome form of scepticism.

Skarsaune thinks the realist can be open to both horns of the dilemma, no matter how pointy they may appear to be. To be precise, he argues that the realist can provide an account of the relation between evolutionary processes and moral truth; and that if this account fails, then they could happily embrace the scepticism conclusion. He also makes some interesting concluding remarks about the nature of moral realism. We’ll look at all three of these elements in what follows.


2. Pain and Pleasure
Skarsaune’s willingness to embrace the two horns of the dilemma stems from his belief that he can provide a pre-established harmony account of the relationship between evolved evaluative judgments and the moral truth. If you have read my series on David Enoch’s response to Sharon Street, this will be a familiar idea, however, I think Skarsaune’s account is slightly more persuasive.

Enoch focused on the correlation between evolutionary goals such as survival and reproduction and deeper moral truths like the intrinsic goodness or badness of pain; Skarsaune focuses directly on the evolutionary utility of pain and pleasure.

He begins by making the following substantive claim:

• P: Pleasure is usually good (for an agent) and pain is usually bad (for an agent).

This claim is agent-relative and non-absolute. It accepts that there may be exceptional cases in which pain might be good for the agent. This possibility does not matter for Skarsaune’s argument, provided such cases are relatively rare.

P can be restated using the language of reasons as follows:

• P*: The fact that x would give the agent (S) pleasure is usually a reason for S to bring about x; likewise, the fact that x would give S pain is a reason for S to avoid bringing about x.

Skarsaune argues that two plausible inferences can be made from P (or P*). The first of these maintains that if P is true, then the first horn of Street’s dilemma is tenable. That is to say, a connection between evolutionary processes and moral truth can be found. The second inference maintains that if P is false, then the second horn of Street’s dilemma is tenable. That is to say, the realist has nothing to fear if P is false because this would imply that an awful lot of what we think we know about morality and about reasons for action would be in error. Realists usually accept such risks of error (indeed, one reason for being a realist is that one accepts the risk of error).

3. The Evolutionary Utility of Pain and Pleasure
Turning our attention to the first inference, we need to understand Skarsaune’s confidence in the connection between evolution and pain and pleasure. Surely, we might argue, evolutionary processes direct us toward that which is fitness enhancing, not that which is intrinsically good or bad?

Yes, responds Skarsaune, but one way in which evolution directs us toward that which is fitness-enhancing is by making things that are evolutionarily beneficial pleasurable and things that are evolutionarily detrimental painful. (You might like to read this series I did on Paul Draper’s evidential argument from evil for related ideas).

It’s easy to see how this is the case in relation to pleasure: the belief that something is pleasurable provides motivation to act; those individuals who took pleasure from evolutionarily beneficial activities were motivated to act in evolutionarily beneficial ways; as a result they tended to leave more offspring than those who did not take pleasure from such actions. Thus, the fact that we associate pleasure with certain activities plays a part in evolutionary explanations of our existence.

So far so good, where do we go from here? Well, we simply point out that P is true - that pain and pleasure are part of the essential moral fabric of the universe - and so evolutionary processes can track the truth of moral states of affair. Problem solved; dilemma dissolved. Right?

Not so fast. Doesn’t this really only imply that evolutionary processes create value? In other words, that evolutionary processes have made certain things valuable to us, and not that evolutionary processes have somehow managed to direct us towards the independently determined moral truth?

Skarsaune has a response. It is true that evolution has created a type of value by using the pleasure/pain mechanism, but we need to be clear about what this is. Evolution has merely made it the case that we find certain states of affairs to be valuable; it has not made it the case that pleasurableness itself is a good. The goodness of pleasure (and badness of pain) is independent of evolution. The distinction is subtle, but essential.

So there is, in effect, a pre-established harmony between the pleasure-seeking (and pain-avoiding) mechanism used by evolution and an independently specified moral truth. This allows the realist to embrace the first horn of Street’s dilemma.


4. What if we are wrong about P?
Not content to rest on the foregoing argument, Skarsaune also thinks he can show that a moral realist should be undeterred by the second horn of Street’s dilemma. The realist might be forced into that horn by someone arguing that P is wrong: that pain and pleasure are not usually good/bad for the agent pursuing them.

Skarsaune asks us to assume, for sake of argument, that this critic is correct. What would follow from this? Only that most of our beliefs about practical reason and morality are false. And presumably if this is the case, we’ll have bigger things to worry about than the plausibility of moral realism.

For example, suppose it were really the case that pleasure did not supply you with a reason for action. This would mean that most of your beliefs about what you have reason to do would be false. Maybe that's not significant since it relates to the agent-relative aspects of pleasure and pain. What about the agent neutral aspects? Well, similarly, the falsity of P would deprive us of many reasons for acting in the interests of others since most of those reasons relate to making the lives of others more pleasurable.

Either way, if P is false, then a lot of what we take for granted is false.


5. Realism and Mind-Independence
Even if Skarsaune’s argument to this point has been convincing, there is one final objection. Indeed, this is an objection raised by Sharon Street in her original presentation of the dilemma. It runs roughly along the following lines:

Sure, we can say that pleasure and pain are valuable and can be tracked by evolution, but in saying this aren’t we renouncing our commitment to moral realism? After all, realism is usually understood to be the view that moral facts are mind-independent. But pain and pleasure are very clearly mind-dependent. So to place them at the centre of our moral theory is to switch from realism to anti-realism.

Skarsaune disagrees. He thinks Street only makes this argument because she has an impoverished conception of moral realism. Realism is not committed to the view that moral facts are entirely mind-independent. We have to be more discriminating in our understanding of what the realists think is independent from what.

To be precise, we need to more discriminating in our breakdown of the various mental states from which a moral fact can be independent. Skarsaune argues, citing the examples of Nagel, Parfit and Shafer-Landau, that realists do not think moral facts hold independently of all mental states. They think that moral facts hold independently of beliefs and judgments, not independently of affective states.

I don’t know what to make of that claim. In some ways, I don't care what those defending realism actually believe. It is often the case that individuals hold beliefs that are inconsistent with the theories they defend. What matters to me are the implications of those beliefs. I think that if what Skarsaune says is true, then there is no important difference between realist and anti-realist theories. This would be an odd result, but I'd be glad to hear that defenders of realism are coming round to my position.