[EM] Better Approval-voting option? Could ABucklin fail FBC?

[Abd ul-Rahman Lomax]

At 04:55 PM 3/1/2012, MIKE OSSIPOFF wrote:

>If you rank your favorite, F,  in 1st place, s/he gets a majority, 
>even though s/he doesn't win, because someone else has a higher
>majority.

That's apparently quite unusual. Even if multple votes in first rank 
are allowed -- they certainly should be -- most voters will not use them.

Sequential approval voting, i.e., a series of polls where voters 
start out with "insisting on their favorite," and then gradually 
lower their approval cutoff until a majority is found, is simply a 
more efficient version of what is standard deliberative process, 
i.e., vote-for-one majority-required, repeated until a majority is found.

In any case, to me, if the number of ballots were not to be limited, 
I'd want to see Range polling, with explicit approval cutoff, plus a 
ratification vote that explicitly approves the result. In some 
organizations, a mere majority margin, thin, really isn't desirable, 
it should be better than that. Popes were elected by repeated 
approval polling, two-thirds majority required. But I'd prefer to 
leave it to the majority to decide what margin is needed. Otherwise 
it is the *rules* which are in charge. I.e., the past is ruling the 
present, which I'm learning is not a great idea, for many reasons. 
Informing and suggesting, yes, but ruling, no.

>A number of people rank F, and, if you help F get a majority, then 
>they won't give a vote to their next choice.
>
>That's regrettable, because their next choice could win with those 
>votes, while F can't win. And when their next choice doesn't win,
>someone worse than s/he (as judged by you) wins.
>
>You got a worse result because you didn't favorite-bury.

Mike, I'm not sure I'm following you here, but the situation, 
multiple majorities in the first round, would be indicative of a 
highly unusual context.

Let's see if I understand. If you vote for your Favorite in first 
place, someone else has a higher majority, call him or her A. In the 
first round? There is a third candidate who has a lesser majority, B, 
whom you prefer to A. If you vote for B in first rank, they might tie 
the other majority candidate. I tend to think of my own votesg as 
being representative of a class of voters, i.e., what I do, others 
may do, so this might flip the result to B, an improvement from my perspective.

But if I really fear this, I can vote for B in first place in 
addition to F. That's not burying, that is normal Approval/Range 
strategy. It's equal ranking, not preference reversal.

The optimal number of ranks in a Bucklin ballot would be such that 
nearly all voters bullet vote in the first rank. It's entirely 
possible that this would happen with three slots, and we can't tell, 
because historical Bucklin was three-slot, but "overvoting" was 
prohibited in the first rank.

When there are more than two viable candidates, I'd expect majority 
failure to occur in the first rank, routinely. The scenario presented 
won't occur, at all, so a voter worrying about it is worrying about 
something quite unlikely.

>So maybe, even if that scenario is merely possible, I shouldn't 
>propose Stepwise-to-Majority unless it turns out that the FBC-failure scenario
>can't happen.
>
>But more worrying is the fact that one could tell that same story 
>about ABucklin (the ER-Bucklin defined at electowiki).
>
>Of course a vague verbal scenario like the above might not have an 
>actual numerical example that can carry it out. There might
>be some reason why such an example couldn't work. Still, it's worrying.
>
>Does anyone know if there's actually a proof that ER-Bucklin meets FBC?

It's an Approval method, so this depends on how you define "Favorite 
Betrayal." If equal ranking is betrayal, yes. But that's weird.

>Can it be shown that the verbal FBC-Failure scenario described above 
>couldn't really happen?
>
>Might ABucklin fail FBC?

I don't see how what you described is Favorite Betrayal, but I 
probably don't realize details of the method you are considering. I 
haven't been reading the list, but "Stepwise Bucklin" sounds to me 
like something I've proposed: using a Range ballot and stepping down 
through the ranks until a majority is found. I'd use such with an 
explicit approval cutoff, and not allow the election to complete in 
one poll if a majority doesn't approve that candidate.

But I'd also do more sophisticated analysis. I'd determine the 
sum-of-votes Range winner as well, and look for a differing Condorcet 
winner. Given the option of an additional poll, either perfect or 
''very substantial'' compliance with the Majority and Condorcet 
criteria is possible, while, at the same time, reducing Bayesian 
Regret to a minimum.

I've been claiming for some time that runoff systems push results 
toward absolute utility maximization, because of the influence of 
real preference strength on voter turnout.