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Poll Results

Poll 121: Contest! You win if "A" is the second most popular choice:

Total votes: 2377

A: 995 (41.9%)  
B: 848 (35.7%)
C: 534 (22.5%)

Almost, but no cigar. Martin Gardner once ran a series on contests such as this in Scientific American. In the examples he gave, it was possible to reason that if everyone voted reasonably, then you could maximise the chances of winning by assigning probabilities to the various options, and randomising your vote according to the assigned probabilities.

As a fairly simple example, imagine if there were two choices, A and B, and the voters win if A gets more votes than B, but less than three times as many. Clearly a lot of people need to vote for A, but you can't just blithely vote for A, because if everyone does that, B won't get any votes and you will lose. So instead, you roll a (standard six-sided) die. If it comes up 1-4, you vote A, on a 5 or 6 you vote B. If everyone is rational, and comes to the same conclusion, A will almost certainly get close to twice as many votes as B, and the voters will win.

Unfortunately for anyone who is familiar with this sort of thing, I deliberately set up this contest so that there was no way to decide objectively between voting for B or C. You want either B or C to get more votes than A, and the other to get fewer votes than A. You could assign a high probability to B, medium to A, and low to C - which would work if everyone did the same thing. But assigning high to C and low to A would also work, if everyone did the same thing... and those two options are mutually incompatible.

The only thing you really have to go on is the psychological difference between B and C inherent in the labels and the alphabetic ordering. So now you start to get away from logic and into the realms of the human psyche. This is a game that Spock cannot win, but that Kirk just might. McCoy would just give up and pick something at random.

So my next question is, are most readers Spocks or McCoys?

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