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In the Random Ballot voting method, every voter writes down their favorite candidate, the ballots are shuffled, one is drawn, and whoever is on that ballot is the winner.

This is said to be a completely strategy-free voting method; there's no incentive to write anyone other than your true favorite. If your ballot is selected, you get whatever you want. If not, you get nothing.

When used in a single-winner contest, it is also strategy-free, in that there is no advantage in tactical voting.

Yet some claim that this creates a prisoner's dilemma, and that it's actually better to coordinate with other voters (of opposing ideologies) and promise to strategically both vote for a compromise candidate to increase your expected value.

Is this a prisoner's dilemma? Is there really an incentive to weaken your vote to increase your expected value? Does it depend on whether a secret ballot is used?

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  • Amazing voting system. Is it actually in force anywhere in the world.
    – Bregalad
    Commented Nov 16, 2019 at 19:25
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    @Bregalad I don't think most people would find it "amazing" or recommend using it in the real world. It's mostly a hypothetical example used for comparing real world voting methods. en.wikipedia.org/wiki/Random_ballot#Prevalence
    – endolith
    Commented Nov 17, 2019 at 3:30

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It is precisely because of the Prisoner's Dilemma logic that random ballot is strategy free.

A voting system being strategy free means that what (you think that) other people's votes have no impact on how you would vote. Since the impact of your vote always is "a tiny chance for your selected candidate to win", you don't need to consider other people at all. You cannot make deals with other voters either, since they are not enforceable. If you would make a deal to both vote for a compromise candidate, each player has an incentive to secretly deviate and vote for their preferred choice after all.

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    Especially since any voter counter greater the v=2 means that if a candidate other than the agreed upon candidate wins, someone reneged on the deal, but only the person who did so can known for sure it was them. Once v>10, it's untenable to even wager an accurate guess, and at v>100, there's zero incentive to bother striking a deal with any other voter.
    – Jesse Williams
    Commented Nov 15, 2019 at 15:16
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Random Ballot could be considered a prisoner's dilemma, depending on what your priorities are.

The Prisoner's Dilemma is a scenario where two people are making a binary choice where the stable equilibrium of the system (the strategic choice of all parties trying to maximize their personal gain) is less profitable for all players than if everyone had made the opposite choice. It assumes that neither participant is able to see how the other is choosing until after both choices have been made.

To analyze the Random Ballot, let's consider a simple system where there are two voters (Alex and Chris), and three politicians (A, B, and C). Alex wants A and dislikes C, Chris likes C and dislikes A, and both tolerate B.

If both voters pick their preferred candidate, then the odds are 50% A and 50% C, with one voter getting exactly what they want, and one player losing out.

If one player (we'll use Chris) decides to compromise and picks B, then the odds are 50% A and 50% B. This is obviously fantastic for Alex, but kind of sucks for Chris.

If both players compromise, then B is guaranteed to be elected.

The stable equilibrium here is for both players to choose their preferred candidate. The probability of your ballot being chosen is independent of what you write on it, so you might as well write your favorite candidate.

This is a prisoner's dilemma if (and only if) both voters consider the guaranteed election of B to be preferable over 50/50 odds of A or C being elected.

If both voters like B almost as much as they like their favorite candidate, then they'd be interested in reaching a compromise, and this becomes a prisoner's dilemma.

If both voters dislike B almost as much as they dislike the other candidate, then they'd probably prefer a 50/50 shot at their favorite over the election of B, and this is not a prisoner's dilemma.

If one voter likes B, but the other does not, then it is not a prisoner's dilemma, because while one voter might prefer B over the 50/50 odds, they know that the other voter does not and therefore has no incentive to vote for B.

Of course, really Random Ballot voting is more complicated than this because there are more than two voters and three candidates, and because you don't perfectly know the desires of the other voters.

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    It's probably worth noting that if there is a secret ballot and more than two voters then this particular Prisoner's Dilemma still leads to everyone being better off unilaterally defecting, i.e. voting their first choice anyway. This is for much the same reason that the standard non-iterated Prisoner's Dilemma gives this result - voting how you want always gives better odds this election, and if no one knows you broke the pact they can't punish you by breaking the pact themselves in the next election, so there's no downside.
    – Princess Ada
    Commented Nov 15, 2019 at 12:18

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