[EM] Chain Climbing

[Juho Laatu]

On 26 Apr 2014, at 02:32, Forest Simmons <fsimmons at pcc.edu> wrote:
> Because of these nice properties I prefer the use of explicit approval cutoffs.  If any voters do not specify an explicit approval cutoff, then their truncations should by default be taken as disapproval,
> 
> The approval cutoffs allow voters greater ability to make their will known.  In some cases they help to discern strong preferences among ranked clones that would otherwise be impossible to express on mere ordinal ballots.  Which is a stronger refutation of putative clone status?  A new candidate D being ranked between C and C' on a few ballots. or an approval cutoff being placed between them on the same ballots?
> 
> Where do we go from here?
> 
Explicit approval cutoffs are a useful feature in the sense that as an add-on feature to rankings they can be used to collect quite sincere additional approval related information (plain approval methods ar less good). I see pure rankings and rankings + approval cutoff as two useful ballot/voting approaches that both can be used as a basis of some very good election metods.

I don't like the intermediate approach of implicit cutoffs (= truncation as approval cutoff) as much since (instead of collecting more information like explicit approvals do) that approach easily encourages voters not to rank the candidates of the "opposite side" at all. This may lead to unwanted results. Your approach of using truncation as approval when there is no explicit approval works however quite ok. I note that in real life one could use ballots where voters rank candidates by ticking one of the columns to the right of the candidate name, and where the ten first columns are green and the rest are red. That should make the approval cutoff very clear to all voters.

The methods should probably expect voting behaviour where voters often disapprove the strongest competitors of their favourites rather than place the approval cutoff in a place where it most accurately reflects their "feeling of disapproval". Or maybe one should say that their feeling of disapproval often follows the probabilities of who might beat their favourite candidates :-).

Anyway, in short, yes, rankings + explicit approval is a useful category of information to collect from the voters, and the analysis that you presented on the possible approaches to using such additional information is a good one.

It may be quite feasible to collect additional explicit approval information from typical voters in typical elections. Even if the additional approval information could in most elections be insignificant in the sense that the winner would be obvious also without considering the approval data, that additional data can be useful for other purposes too, like deriving additional statistical information, or interesting news for media, or allowing voters to express their approval and disapproval of various candidates. Having an explicit non-approved section may also encourage voters to rank all candidates (= at least all potential winners), which is a very good thing in ranked methods.

Juho


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