[EM] disappointment vs. regret

[Forest Simmons]

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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