[EM] What are some simple methods that accomplish the following conditions?

Juho Laatu juho.laatu at gmail.com
Sat Jun 29 07:43:29 PDT 2019

Some comments on approval cutoffs. I just recently had to think about approval cutoffs a lot when I wrote about ranking methods with additional input (under title "Modified Overall Preferences"). I'll comment from that point of view, but my comments might be useful also in a more general sense.

First of all, I like plain rankings, and I think they are in most cases very sufficient. I thus feel that often approval cutoffs are not needed, and may mean just added complexity to the method and to the voters.

But I analysed the possibility of taking more input from the voters, in the form of allowing them to influence the overall strength (not direction) of different pairwise preferences. Instead of letting the voters have comments on every single pairwise preference relation (or just that linear sequence of relations that the voter wrote in the ballot paper when ranking the candidates), it seemed quite natural to reduce their influence to giving only one approval cutoff. The interpretation would be that candidates above that cutoff would be considered favourites whose defeats to each other should be considered "softer" than the other defeats. That approach seemed to be quite enough for most needs that I could identify. Now, let's see if that kind of a cutoff approach could be somehow useful.

In the method (http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-June/002262.html) rankings determine the (potentially cyclic) preference order of the electorate. The approval cutoff (or any other preference strength modifications) influence the end result only when there are cycles. This means that voters really need not use the cutoff feature. On most cases it doesn't have any influence on the outcome. The cutoffs may however influence the outcome in a meaningful way when there are sincere or strategically created cycles.

The "favourite" cutoff can be used quite efficiently as a defensive measure (this was one of my key learnings). That is positive in the sense that in case (with big "if") there is a need to defend against strategic voting, there seems to be no need to modify the rankings. It is enough to just se the approval cutoff right. The approval cutoff may thus help in making the actual rankings more sincere. I note briefly that in burying scenarios (of three candidates) it doesn't make sense to the strategists to use the cutoff to help the candidate that they rank second, but it may make sense to others to do so. (Alternatively some voters may stop helping (approving) the strategic candidate.) It seems that this is enough to thwart any this kind of strategic attempts (three candidates, with one strategist) (with sufficiently large defence strength parameter k).

It seems that the correct strategy in placing the approval / protection / favourite cutoff is quite simple. The first recommendation is to place it sincerely so that one supports one's favourite group of candidates, i.e. those that one is happy to see as winners. In the case of defending against a (three candidate) burying attack it seemed that one should extend that to cover also the (expected Condorcet) winner that is about to be buried. That is still quite natural, and corresponds to the classical Approval strategy of approving at least one candidate that is a potential winner, and with the natural idea of protecting the candidate that needs protection in this case. My point here is that it seems that setting the approval cutoff is quite natural and sincere (and that in most cases it doesn't matter much even if one would not set any cutoff at all). As a bonus one might get some defence against strategies, while keeping the rankings and more or less also approvals sincere.

In summary, this approach seems to offer a quite natural way of using the cutoff option. Having the cutoff there helped in keeping the actual rankings sincere. Also the cutoffs are quite sincere (indicating "sincere clones" in most cases, and protected candidates in the rest). Having a strong defence capability against (certain types of) strategic voting keeps the votes more sincere than they might otherwise be, since also the strategists will know that they might have no chance in using such strategies successfully. And if this makes the rankings and approvals sincere, we will get also useful information on the voter preferences (not jut strategic votes that are more difficult to interpret). It is also possible to use such method so that most voters do not use the approval cutoff at all, but it would be there in case it would be needed one day (when someone tries to implement dirty strategies).

I still feel that in most elections approvals (or possible richer capability of modifying the preference strengths) are not needed. But having that option may not cost too much. A simple approval cutoff might keep the complexity of the ballots still manageable to average voters. That's all the two cents I have in defence of sometimes possibly using simple approval cutoffs.


P.S. I don't like the plurality criterion. It actually sets an implicit approval cutoff at the end of the listed candidates. The worst part of that idea is that it encourages voters not to rank the candidates of the competing groupings. That (potentially huge amount of missing information) is not good for ranked methods. If voters learn to use that feature, methods might not elect the best winner (sincere Condorcet winner).

> On 29 Jun 2019, at 13:08, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> On 11/06/2019 00.23, C.Benham wrote:
>> On 8/06/2019 7:24 pm, Kristofer Munsterhjelm wrote:
>>>   ..I very much prefer methods that don't need Approval cutoffs.
>> Kristofer,
>> Why is that?
> My objection to (relying too much on) Approval cutoffs is similar to my
> objection to Approval itself. It's hard to determine where to put an
> explicit Approval cutoff, and an implicit Approval cutoff can limit the
> method too much. In either case, it becomes harder for a honest voter to
> fill in the ballot in a way that he won't regret later on.
> There are multiple sincere Approval ballots, so the honest voter doesn't
> know, ahead of time, which he should answer without using some
> heuristic. In contrast, ranking is easy: the voter can just start from
> the best and rank in order. Determining what that order is may require
> some thought, but there's less of a burden finding out just how that
> information should be rendered to the method itself.
> That wouldn't be so much a problem if the method is lenient with noisy
> input; if the ambiguity in where to put Approval cutoffs is like the
> ambiguity in where to equal rank. I think that's why a criterion like
> Plurality seems useful: it gives something extra if voters use
> heuristics close to some intuitive idea of what approving a number of
> candidates means, but doesn't get it wrong if the heuristics are
> slightly off. In contrast, Approval requires that honest voters get the
> distinction just right: if the voters put the cutoff too low, then an
> unwanted compromise wins, but if the voters put it too high, then the
> lack of compromise makes someone from the other side win.
> So to sum up, I guess a reason I don't like Approval is because it
> burdens a honest voter too much; and the reason I don't like Approval
> cutoffs is that, at least if implicit, they transport that burden over
> to the method in question.
> It's possible that a method may use Approval cutoffs yet be lenient
> enough (i.e. more like how the Plurality criterion behaves than how
> Approval itself behaves). In that case, I suppose they're okay. But it's
> not easy to know, from the ballot format itself, which it is.
> (Perhaps one indication of such is whether the method works if nobody
> uses the approval cutoff indicator, or everybody places it at the very
> top or very bottom. Methods that pass Plurality still work if every
> voter ranks every candidate, but Approval would give a perfect tie.)
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