Assertion as a Game

There has been a lot of ink spilled over what assertion is, what its norms are, how it relates to belief, and how in turn belief relates to credence. Here I just want to point out that if it is a lot more advantageous to have turned out to be right about an assertion than its negation, it can make sense to make that assertion even if you think it is unlikely to be true.

For instance, maybe it is more fun to turn out to be right about a claim of conspiracy C than to turn out be right that there was no conspiracy. Turning out to be right about C is just to have asserted C and for everyone to later find out that C. Besides it being more fun to be right about C than to be right about \neg C, it might also make you seem wiser since it was a low probability event that only a select few predicted while everyone else thought that \neg C was obvious. Turning out to be right about C might also be damaging to your political opponents, while turning out to be right about \neg C is not.

So, assuming that everyone finds out what was actually true eventually, say we have that:

\displaystyle U( C  \wedge  \text{I asserted}  \ C) = 90 \\  U( C  \wedge  \text{I asserted} \  \neg C) = -10 \\  U( \neg C \wedge  \text{I asserted} \ C) = -10 \\ U( \neg C \wedge \text{I asserted} \  \neg C) = 20

In this case it makes sense to assert that C whenever P(C) \geq 0.1. Notice that for propositions that are more unlikely, it is more advantageous to have turned out to be right about them, since the asserter will seem wiser for it.

There are many other kinds of practical considerations one might take into account when deciding what to assert. For instance, maybe there is an inquisition going on, and everybody who makes a certain kind of assertion is punished while everybody who asserts its negation is rewarded. I don’t think I need to spell out why it makes sense to assert the negation even if it is very unlikely in that case. What makes the particular kind of practical consideration pointed out above interesting is that the payoff of asserting C depends on whether C turns out to be true.

Since assertion is an ancient and likely evolved practice, we should expect that we expert assertoric practitioners are very good at playing this game. You might think that a difficulty here is that asserting C when you assign P(C) = 0.1 seems a lot like lying, but as the saying goes, the best way to deceive others is to deceive ourselves. Seeing how advantageous it would be in a game like the one above to deceive others into thinking we genuinely believe C, it would be no surprise if we evolved to deceive ourselves into thinking that we believe it too.

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