Wolfgang Schwarz :: Is Selecting By Salience Rational?

Is Selecting By Salience Rational?

Posted on Wednesday, 21 Jul 2004.

Suppose you and I both face a choice between several different options. Say, we both have to pick a ball out of a bag of 100 balls. We win a prize if we make the same choice. But we have no means to communicate. Moreover, our only relevant interest is to win the prize, otherwise we are completely indifferent about the options.

If one of the options is somehow salient, say one ball is red and all the others white, most people will choose that one. And wisely so, as many people following this strategy win the prize, whereas hardly anyone picking a white ball does. However, is this a rational decision among perfectly rational agents who know of each other's rationality and preferences? (I also assume that the agents know that they make exactly the same judgements about salience.)

On the one hand, as a perfectly rational agent, you should make your choice depend only on what you expect me to choose. Since by assumption you have no interest in red as opposed to white balls, or in salient as opposed to non-salient options, these features should not affect your choice at all. So it can only be rational for you to choose the salient option if you have reason to expect me to choose that option. Without such a reason, you should be completely indifferent. But you know that I am just as rational as you are, and that I have just the same preferences. So you know that I will choose the salient option only if I have reason to believe that you will choose it, which I have only if I have reason to believe that you have reason to believe that I will choose it, and so on. Nowhere in this chain of considerations will any of us find a reason to believe that the other has reason to believe that (etc.) any of us will choose the salient option. So we should be completely indifferent.

On the other hand, we both know that if a) we both choose the most salient option, we'll surely win; whereas if b) at least one of us chooses at random, our chance of winning is quite small (.01 in the 100 balls case), no matter what the other does. Assume for the moment (a) and (b) are the only possibilities. Then I should rationally choose the salient option unless I'm dead certain that you choose at random, in which case I should be indifferent. But what could make it absolutely certain for me that you choose at random? Being as rational as I am, you will choose at random only if you have reason to believe -- in fact, are dead certain -- that I myself will choose at random. And you have reason to believe this only if you have reason to believe that I have reason to believe that you will choose at random. And so on. Nowhere in this chain of considerations will any of us find a reason, let alone a decisive reason, to believe that the other has reason to believe that (etc.) any one of us will (certainly) choose at random. So we should both go for the salient option.

Unfortunately, (a) and (b) aren't the only possibilities. Instead of choosing at random or choosing the most salient option, I could also choose the least salient option (if it exists -- it may share the fate of the least uninteresting number), or the option of which I think it would most remind Tony Blair of Paris. What favours selecting by salience over selecting by such gerrymandered properties? Should we choose selecting by salience because salience is, er, the most salient property to select by?

Comments

# Mike S on 29 July 2004, 14:54

We have a common prize winning interest. We know this. If two individuals choose randomly the chances of choosing the same ball are 1 in 100. If they both choose the red then the chance is 1 in 1. We should attribute the other person with the wit to realise this.

# duncan on 29 July 2004, 20:59

Huh. Can I be bold enough to propose that of the subset of intelligent observers, only a philosopher following your line of reasoning would even consider picking anything other than the red ball.

Perhaps therefore the reasons why a philosopher might consider picking a white ball would be an interesting topic for further consideration!

[Found your blog via discussions regarding pingbacks.]

duncan from http://babbage.tv

# wo on 30 July 2004, 09:44

> Can I be bold enough to propose that of the subset
> of intelligent observers, only a philosopher
> following your line of reasoning would even
> consider picking anything other than the red ball.

Agreed. Most people have a tendency to pick the salient option without having worked out a good argument for why that's the best option. This irrational tendency gives everyone else a good reason to also pick the salient option. But what if people didn't have any such irrational tendency, and knew about that?

Mike, isn't your argument just the one I proposed? It works only if selecting by random and selecting by salience are the only two options. But they aren't. Assume the balls have little numbers written on them. Why not pick the white ball with number 34? After all, we know that if we both pick it, our chance of winning is also 1.

(Perhaps it matters whether all or some of the other options have marks which the agents both notice and of which they know that the other will notice it. My guess is that it doesn't matter. But anyway, in real cases that condition is usually satisfied.)

# Mike S on 12 August 2004, 15:03

I had a particularly sleepless night last night and for some bizarre reason started to think over your point, which, as you indicate above, I missed first time around.
I think the issue here is that salience can be, and in real life is more often than not, a relative quantity. Consider 99 white balls numbered 1 to 99 and one red ball. In this instance each ball is salient to some extent, but the red ball could be considered more salient because it has less in common with the other balls than they have with each other.
A more interesting example would be 98 white balls numbered 1 to 98, an unnumbered red ball and an unnumbered white cube. We could perform an experiment to see if difference in shape is more salient than difference in colour. One might think that this would only demonstrate the subjective prejudices of the test group, but it is possible and, I think likely, that there might be a causal relationship between the salience of some attributes and the evolutionary psychology of the test population. I am suggesting here that salience is by definition dependant upon the subject(s). Under the game conditions you initially proposed:
'Suppose you and I both face a choice between several different options. Say, we both have to pick a ball out of a bag of 100 balls. We win a prize if we make the same choice. But we have no means to communicate. Moreover, our only relevant interest is to win the prize, otherwise we are completely indifferent about the options.'
I would assume that as both you and I are human beings (unless you have just passed the Turing test) there will be considerable similarity in the degree of salience we ascribe to a range of attributes.

Wolfgang Schwarz

Is Selecting By Salience Rational?

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