[EM] Honest equal-rank/truncation?

[Kristofer Munsterhjelm]

On 6/19/22 1:09 AM, Forest Simmons wrote:
> 
> 
> El sáb., 18 de jun. de 2022 6:29 a. m., Kristofer Munsterhjelm 
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> escribió:
>> 
>>     A thought about how honest equal-rank might be defined. Earlier I've
>>     said that a good way to define a honest ballot is to find a randomized
>>     strategyproof system that induces it (e.g. Random Ballot for
>>     single-mark, Random Pair for strict ranked, possibly some transformation
>>     of Hay for VNM utility ballots).
>> 
>>     How about this as a starting point?
>> 
>>     "Random Approval": Voters provide Approval-style ballots. Choose a
>>     ballot at random. If this ballot approves a single candidate, then elect
>>     that candidate. Otherwise eliminate every non-approved candidate and
>>     draw another ballot (without replacement). Ignore ballots only approving
>>     eliminated candidates. If every ballot is visited, choose at random a
>>     candidate from the winning set.
>> 
>>     The optimal strategy seems to be to just designate your favorite, 
> 
> 
> Not neccessarily.
> 
> Suppose honest preferences are
> 
> x: A>C>>>B
> y: B>C>>>A,
> 
> where x-y is the voter's subjective random variable with estmated mean 
> near zero and estimated standard deviation at about 2 percent of x+y.
> 
> If that by itself is not enough to make the voter approve C, what if 
> less than 51 percent approval for the winner required fallback from 
> random approval to random favorite?

I think I see your point. If your preference is A>C>>B and the other 
guy's is B>C>>A, then if the other guy gets picked first, then a 
favorite-only ballot of yours won't be counted because A intersect {B,C} 
is empty.

So perhaps I was being too clever. What I was thinking of was that 
equal-rank honestly (regardless of other votes) makes sense if:

- You have dichotomous preferences (Mike Ossipoff's u/a model),
- you have tiered preferences (e.g. these candidates are all excellent, 
these candidates are all good, these candidates are all poor), or
- you don't have time to find the exact ordering, e.g. your preferences 
are something like A>B>>>>C>>>>>>>>D and you vote A=B>C>D.

I think just random favorite with equal rank would preserve this on the 
top end (e.g. preserve equal-rank among the top candidates). That's the 
method that picks a random candidate among a random voter's top-voted ones.

But the method is secondary. Are there other reasons to honestly 
second-rank? If so, then the mechanism should be adapted to reveal those 
as well.

-km