[EM] Approval-Strategy article at CES website

[Juho Laatu]

> On 04 Nov 2016, at 03:30, Michael Ossipoff <email9648742 at gmail.com> wrote:
> 
> First, two things: Most of what I've said about the top-set was meant to be about the strong top-set.
> 
> 1.
> 
> I say that, for most people, based on what they say they want, don't want, and don't like, there are, for them, a strong top-set and a strong bottom-set.

I guess you can say that's typical for all people in all democracies. The strength of those groups varies of course.


> 
> But, as you said, in the general case, not specific to any country, or to any era, but, instead, just hypothetically, a voter might not have a strong top-set, or even a top-set.
> 
> 2.
> 
> When you speak of normal Approval strategy, I presume that you're referring to expectation-maximizing strategy for the general case, when there might not be a top-set or a strong top-set.

Yes. And even if one has a strong top-set and a strong bottom-set, the normal approval strategy would help in casting an efficient vote, even if the person would prefer to cast a vote that is not optimally efficient (from the expectation-maximizing point of view) (but optimally best for him/her in some other way).


> 
> Of course that strategy has been described or proposed in many forms.
> 
> In general, I'd say that it means approving down to the CWs, if there is one, and if it's known or guessed who s/he is. Or, if there isn't one, or if it's a 0-info election, then approving down to the expected winner-merit, however estimated.

If there is a CWs (sincere Condorcet winner, as derived from the preferences of the voters when voting in the actual approval election), and all other voters are assumed to use the normal approval strategy, and all voters are assumed to base their voting decision in sufficiently accurate information on what the preferences of the voters are, then it makes sense to put the approval cutoff next to the (assumed) CWs. (When discussing poll based strategies, one has to take into account also possible distortions in all the assumptions.)

A simple example might be helpful here. Let's say there are seven candidates in a linear opinion space. A1, A2, B1 and B2 are strong candidates (e.g. democrat and republican), and all three C candidates are weak in the sense that they have very little first preference support. The linear opinion space is A1 - A2 - C1 - C2 - C3 - B1 - B2. C2 is the CWs. A supporters should put their approval cutoff between C2 and C3. B supporters should put their approval cutoff between C1 and C2. C2 will be elected. I guess this is what you meant with "approving down to the CWs".

Note that this theory does not hold if we assume that some voters vote based on their personal preferences only (e.g. their top-set and bottom-set), or that they do not have accurate information about the preferences during the election day. In real life that "accurate information" can of course be only approximate information that the voter has derived e.g. from the polls and other pieces of information during the days leading to the election.

And then back to the poll strategies. The strategic plan of party A includes of course the target to make C1 or A2 the winner instead of C2 (or someone worse). It is difficult for the B supporters to decide where to put their approval cutoff. Why not tweak the poll results a bit (by supporters giving appropriate false information in the polls, or maybe by publishing false/modified polls). That might make some of them approve also C1, and maybe also A2. Or at least the C2 and C3 supporters might do so. Since C party is small, small changes in balance might lead to important changes in the outcome. It is quite possible that A2 will win as a result of the applied strategy.

. . .

> CES is going to do a poll, to test the various voting systems in a big national poll. Instead of doing it themselves, they're going to hire a company to do it, a company affiliated with the Associated-Press  :^ |

A typical poll in Finland is one that has been ordered by some major newspaper or other media, but from from some well known neutral (possibly international) research company. The name of the company that implemented the poll and error margins are always mentioned when the poll results are published, to keep the trust level up.

. . .

>   Typical voters take into account their experience in life, results of previous elections, all the polls that they have seen (with emphasis on those that they consider reliable), and then make their educated guess on who the potential winners are.
> 
> Yes.  But, here, it's best for most people (who never hear about the more reliable small-organization polls) to regard elections as entirely 0-info.

If you have some semi-reliable or vague info available, you probably use it to the extent that its reliability level justifies.

. . .

> All points of view would be heard, and the "lesser-evil" advocates would be laughed off the stage.

The normal approval strategy includes the notion of "lesser evil" since the voter doesn't necessarily like the frontrunners.

. . .

> There can be an approval election with exactly two potential winners. In this situation the election is in practice just an election between two candidates (if we focus only on the question who will win this time).
> 
> No. If a voter has a strong top-set and a strong bottom-set, and both of your alleged frontrunners are in the bottom-set, then the voter won't approve either. Hir optimal strategy is to approve (only) hir strong top-set.
> 
> ...because polls, even if they were honest (Dream on), aren't 100% reliable.

You must be saying that this voter assumes that the polls are not reliable, the voter knows better himself/herself, or guesses, and therefore put his approval cutoff in some other place. I'd say that this voter thinks that the two (or any number of) potential winners are different ones than the real ones (that we assumed above), and therefore votes in a way that makes his/her vote void. The voter did not manage to make a difference in the only relevant question, which one of the two potential winners to pick. He/she was mistaken on what his/her optimal vote was (continuing to assume that we now know that only the two mentioned candidates had any chances to win).

. . .

> Those voters that approve only one of those candidates will have a say in this election. Those voters that approve both or none of them will have no say in this election.
> 
> I assure you that they couldn't care less which of two unacceptables wins.
> 
> If that's what the "election" offers,  they won't mind not having a say in it.

Quite possible. And leads to casting a vote that has no influence on who will be elected in this approval election.

. . .

> By normal strategy, you mean an expectation-maximizing strategy when there is no strong top-set or strong bottom-set.

The normal strategy can be used with or without having / identifying strong top and bottom sets.

> 
> But, when there is a strong top-set and a strong bottom-set, then the normal strategy, and the strong vote, the only strong vote, _is_ to approve (only) your strong top-set.
> 
> So there's no conflict or distinction between normal strategy & strong vote, vs approving only all of one's strong top-set when there is one.

If someone bases his/her decision on where to put the approval cutoff only on his/her personal preferences, without taking into account who the potential winners are (if any half reliable such information is available), then some votes are probably not strong / efficient in the sense that they would influence the outcome of this election as strongly as possible.

Juho



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