Tomas McIntee
3 min readApr 17, 2022

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It's a fair point. ABOC and BAOC are more stable strategic votes than ACOB, and the A > C > B and A = C > B scenarios can be seen as the main cases in which O-third Borda votes correspond to bullet approval votes - because of the risk that you've completely overestimated the support for the apparent leader due to a late collapse.

Here are the three reasons to expect ACOB votes instead of AOCB votes in those situations. There's a basic reason, a "smart" reason, and a "dumb" reason.

The basic reason is that in the A > B > C event, the decision to Borda-bury B is *already* hedging against an unlikely event. It's just that it's still an obvious strategic move to make, and there isn't a compelling reason not Borda-bury B. So why even think about the tiny estimated chance of C winning?

The dumb reason is that the best overall functional but simple Borda bury technique is to just modify your ranking by identifying the top two candidates, rank one top, rank one bottom, and stuff the rest in the middle. This is the heuristic that's intuitive, works, and isn't complicated.

Exactly what to do with three candidates in closer contention (A = B = C) in a larger set is less intuitive; the robust heuristic is to *spread* the viable candidates versus *burying* viable candidates, a distinction that emerges with five candidates, e.g.:

A > O1 > B > O2 > C

On the other hand, the "bury" heuristic is simpler ... so people might instead rank:

A > O1 > O2 > B > C

Even though it's worth trying to make sure you have a half-vote towards B > C in the event that the result resolves to B = C > A.

This is the same reason why C > A > B will tend to get a "strategic" bullet vote instead of a strategic AB vote, even though that's rationally more likely to be an unexpected C = B > A than an unexpected A = B > C. The typical strategic heuristic for approval voting means that an A-first-choice voter never votes for anyone expected to do worse than A, even though it can backfire in rare expectations.

Similarly, with A = B = C, the decision to rank ABOC or AOBC, and conversely to approve A or AB, ought to be based on preference intensity, but will usually just follow a heuristic. AOBC / A match the typical heuristic better, but aren't always the best vote.

The smart reason is that strategic reasoning doesn't stop at the first level. You have to consider what happens when others adopt the same strategic ballot, and you have to consider the nature of your errors. You should rationally assume that there's at least a tail risk that a large number of voters adopt a similar strategy.

Someone who ranks O in second should be considering the possibility that both they have public opinion wrong *and* that there are many strategic voters who have brought all candidates into close contention by similarly ranking O second.

Basically, in a Borda vote, the higher-level strategic threat is that there's a tail risk of A = B = C = O, it's hard to evaluate that tail risk relative to what is already a monumental upset of expectations, and the result of O winning is considered to be an extremely bad event.

So, for example, if one rationally estimates a 1% chance that C (bah, basically decided!) and an 0.1% chance that O is in close contention (almost unimaginable!), it's worth hedging against O a little bit in that tail event.

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Tomas McIntee
Tomas McIntee

Written by Tomas McIntee

Dr. Tomas McIntee is a mathematician and occasional social scientist with stray degrees in physics and philosophy.

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