[EM] disappointment vs. regret

[Kevin Venzke]

 I don't hate the idea of giving the favorite candidate more flexibility. Candidates would either indicate their approvals in advance, or wait for the second round and then figure it out (simultaneously?). I guess I don't see how to avoid the scenario where candidates themselves play chicken with this.
I do like that if the second round is presented as delegating a decision to a single candidate, the math can be kept off the ballot. You could do everything in a single round expressing a single vote, and task the candidates with approving each other according to the weighting requirement.
On your actual topic, I have to say, I am skeptical of defining disappointment for individual steps of a multi-step process. I'm wary that the process could do something to respect that some % of voters are disappointed to see a tentative winner status switch from candidate A to candidate B, when an honest assessment will show that A could never be the winner of the whole election. In that case the "disappointment" measured for these voters is a little abstract.
Kevin

    Le vendredi 21 février 2020 à 18:15:31 UTC−6, Forest Simmons <fsimmons at pcc.edu> a écrit : 
 Giving the favorite candidates a little more flexibility might help them to thwart "chicken" gamers.

On Fri, Feb 21, 2020 at 4:02 PM Forest Simmons <fsimmons at pcc.edu> wrote:

Kevin,
Thanks for your comments and catching that snafu.  It turns out that if you just impose that truncated candidates get zero approval, the method is still monotonic (and clone free to the same extent as range is provided equal ranking and truncations are allowed).
I like the idea of two rounds ... one to establish the firstplace/favorite preferences, and the other for determining the approvals informed by the information garnered in the first round.  It seems like the less sophisticated voters might be happy to delegate their second round votes to their favorite or to some other published preference order.
In the case of the published order the approvals would be filled in automatically according to the rules we have been contemplating.  Perhaps the delegated favorites could have a little more flexibility???
You probably remember Joe Weinstein.  A long time ago he suggested that instead of basing your approval cutoff on expected utility of the winner, you could use the 'median probability" idea; if your subjective probability sense tells you that the winner is less likely to be someone that you deem to be better than X than otherwise (someone you like no better than X), then approve X.  

When I first thought about using that heuristic in a DSV setting, I ended up with non-monotonic methods based on multiple rounds.  Eventually all of the probability got concentrated in the top cycle, and further rounds continued around the cycle.  At that point it was the same as Rob LeGrand's approval strategy A (foreshadowed by Weintein's remarks when he first introduced his idea).  

Another way of looking at the problem is that the winning probabilities (based on previous rounds or on sets of sampled ballots) never stabilized, so how could you define "THE winning probability."

But when we replace the nebulous subjective probabilities with the well defined first place preference distribution, then we have something more definite to go on, and we get a monotonic method!

Changing topic slightly back to the idea of disappointment;
In the definition of disappointment "felt by" ballot B when the champion changes from candidate X to candidate Y, I wrote...
If candidate Y is ranked above X, then the disappointment is zero.  It should have said "above or equal to X," since equal is no worse, hence no disappointment in this sense. Nevertheless, if candidate Y is truncated on ballot B, then B should be counted as having 100 percent disappointment even if X was also truncated, and even if the random ballot probability of a candidate being ranked (i.e. above truncation) on ballot B is less than 100 percent.
Thanks Again,
Forest


  

  
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