[EM] disappointment vs. regret
Forest Simmons
fsimmons at pcc.edu
Fri Feb 21 16:15:00 PST 2020
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
>
> On Thu, Feb 20, 2020 at 8:59 PM Kevin Venzke <stepjak at yahoo.fr> wrote:
>
>> Hi Forest,
>>
>> I like this method, though it seems to contain a huge gotcha. If you
>> truncate candidates who collectively have more than half of the random
>> favorite win odds, your ballot will approve everyone. I imagine this is
>> deliberate and a big reason why a pre-election poll is envisioned to help
>> inform the voters.
>>
>> I have been sitting on a similar idea for a long time and maybe I should
>> just write it out now.
>>
>> I had the thought that if you have an approval election where voters are
>> required to approve a majority of the options, the "median" one of those
>> options could be expected to get 100% approval. (Exceptions for strategic
>> voting and the possibility that there is no underlying issue space to
>> explain the preferences.) Whichever option gets the most approval would be
>> your best guess for the median.
>>
>> On reflection this seems not actually right, since the options could all
>> be located far from all the voters so that multiple options get 100% and
>> none of these are the median option. But no matter, this issue is quickly
>> fixed.
>>
>> If we want to apply the idea to find the median VOTER (and his preference
>> for the outcome), the options need to correspond to or be weighted by the
>> voters themselves. Using first preference weight (identical to random
>> favorite win odds) seems like a reasonable way to weight the options, since
>> in issue space the voters should be closest to their favorite candidate.
>>
>> You could explain this requirement to approve a specific minimum value of
>> options, as an analogy to proposing a coalition to form a government. A
>> viable proposal for a ruling coalition (usually) has to cover a majority of
>> the voting power.
>>
>> What is the expected effect? If the electorate is split 51-49 between two
>> factions, but there are actually candidates near the median (which we might
>> expect, due to the increased viability of such candidates), then basically
>> the winner will come from the 51, but the 49 will choose who it is. This is
>> in contrast to the 51 and 49 factions "privately" selecting one best
>> nominee each, allowing the median voter to choose which nominee wins. In
>> that case, as we see, the median voter is part of the winning faction but
>> is normally an extremist within that faction.
>>
>> I do think the concept has a serious risk of electing a candidate who
>> doesn't really have any support.
>>
>> You could have a separate round of voting in advance to determine
>> reasonable finalists, or you could do the entire thing in one go, deduced
>> from a single set of fully ranked ballots.
>>
>> A two-round approach probably gives the voters a greater sense of agency.
>> If they know the candidate weights, they know how their second round ballot
>> is going to get interpreted. If they want to try a strategy, they at least
>> can tell what they're doing. A downside is trying to figure out how to
>> present the math to the voter.
>>
>> In terms of ballot format, the simplest possible presentation of the idea
>> is to have two rounds: One round narrows the field somehow to three
>> finalists, and the second round is effectively Majority
>> Favorite//Antiplurality. I.e. in the second round, you have to rank all
>> three candidates. A majority favorite wins. Otherwise everyone approves two
>> of the three options. (Half-approval for the middle option would also be
>> recognizable as following the principle.)
>>
>> I don't have a name for the idea yet. Something about the mandatory
>> nature of suggesting a coalition seems appropriate. But one might point out
>> that the method doesn't actually identify any coalition, and the whole
>> thing is just a means to guess where the median is.
>>
>> Kevin
>>
>>
>>
>> Le jeudi 20 février 2020 à 17:15:26 UTC−6, Forest Simmons <
>> fsimmons at pcc.edu> a écrit :
>>
>>
>> Here's a method that I consider to be good in its own right, not only as
>> a starting point for "Minimum Disappointment Covering Enhancement."
>>
>> Assume ranked preference ballots with equal ranking and truncation
>> allowed. Also assume access to a "random favorite" probability
>> distribution, whether from a separate poll or by inference from the ballot
>> set itself.
>>
>> A ballot B is said to "like" candidate X if a random favorite is less
>> likely to be ranked ahead of (i.e. above) X than not on ballot B.
>>
>> The method elects the candidate liked by the greatest number of ballots.
>>
>> This method is monotone whether or not the random favorite distribution
>> is computed on the fly.
>>
>> It also satisfies clone winner and clone loser the same way that range
>> voting does, i.e. as long as the clone sets are ranked (or truncated)
>> together.
>>
>>
>>
>>
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