[EM] disappointment vs. regret
Kevin Venzke
stepjak at yahoo.fr
Thu Feb 20 20:59:43 PST 2020
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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