[EM] How to find the voters' honest preferences

[Kevin Venzke]

Hi Forest,

>________________________________
> De : Forest Simmons <fsimmons at pcc.edu>
>À : EM <election-methods at lists.electorama.com> 
>Envoyé le : Samedi 7 septembre 2013 19h50
>Objet : [EM] How to find the voters' honest preferences
>
>The following method makes use of two ballots for each voter.  The first ballot is a three slot ballot with allowed ratings of 0, 1, and 2.  The second ballot is an ordinal preference ballot that allows equal rankings and truncations as options.
>
>The three slot ballot is used to select two finalists: one of them is the candidate rated at two on the greatest number of ballots.  The other one is the candidate rated zero on the fewest ballots.
>
>
The runoff between them is decided by the voters' pairwise preferences as expressed on the three slot ballots (when these finalists are not rated equally thereon), or (otherwise) on the ordinal ballots when the three slot ballot makes no distinction between them.
>
>[Giving priority to the three slot pairwise preference over the ordinal ballot preferences is necessary to remove the burial incentive.]

Good job there.

Except for the way you determine the runoff finalists, it reminds me of what I named Single Contest.

( http://wiki.electorama.com/wiki/Single_Contest )

>
>Note that there is no strategic advantage for insincere rankings on the ordinal ballots.

You seem to have a problem with majority favorites on the second ballot: They might not get elected. My method has this problem as well; I propose a majority favorite check, but this is inelegant and means there is strategy in the ranking component. (Well, both methods have strategy there anyway, since the ballots either must conform to each other or are interpreted as conforming to each other. I don't think you stated it was required for the second ballot to not reverse preferences of the first ballot.)

The advantage of your method over mine seems to be that you don't need a special rule to ensure that a candidate with a majority of top-ratings on the first ballot will make it into the runoff.

On the whole I do think my method for picking finalists is better. I can reword it for the context of cardinal ratings as opposed to approval:

For every pair of candidates X and Y (where X is not Y) sum over all voters the better/greater of the two three-slot ratings given by that voter to X or Y. The sum is the pair's score. The finalists are the pair of candidates with the best score.

This pair score is an estimate of which pair the electorate would like to see in the runoff. If you love a candidate then you love all of his pairings. If the best candidate in a pair is just OK, then that pair is just OK as well. If you don't like either candidate in a pair then the pair is bad.

Is this really how the voter feels? Perhaps not, but it is difficult to cheat: If you fear A will lose in a runoff with B, the only way to weaken this particular pairing (hoping A can get a more advantageous one) is to lower your A rating. This is not a very promising strategy, especially if your runoff vote must not contradict your pair vote.

>Questions. 

>
>(1) What are some near optimal strategies for voters to convert their complete cardinal ratings into three slot ratings in this context?


My concern is that your selection method (basically "loved by most vs. hated by least") can grab the same candidate, which makes the runoff moot and creates an incentive to exaggerate so as to potentially bypass the runoff. If strategists fail, they are probably not harmed, but the expressiveness of their ballots is reduced.


>(2) We have a "sincere approval" method of converting cardinal ratings into two slot ballots.  What is the analogous "sincere three slot" method?
>
>[Sincere approval works by topping off the upper ratings with the lower ratings;  think of the ratings as full or partially full cups of rating fluid next to each candidate's name.  If you rate a candidate at 35%, then that candidate's cup is 35% full of rating fluid.  Empty all of the rating fluid into one big pitcher and use it to completely fill as many cups as possible from highest rated candidate down.  Approve the candidates that end up with full cups. This is called "sincere approval" because generically (and statistically) the total approval (over all voters) for each candidate turns out to be the same as the total rating would have been.]


If I understand this correctly then this means that if you rate one candidate 100%, one candidate 99%, and then a dozen candidates at 0%, you will approve only the candidate at 100%. Can that be right?

Kevin Venzke