[EM] Juho,5/25/12, roughly 2230 UT

[Juho Laatu]

On 24.5.2012, at 5.40, Michael Ossipoff wrote:

> > If it’s a u/a election, and if Compromise is the only acceptable who can beat the unacceptables, then rank Compromise alone in 1st place.
>  
> Maybe one can build an implementable strategy from this one. Some further definitions are however needed. What is the definition of and how will the voters determine if the election is a u/a election?
>  
> [endquote]
>  
> An election is, for you, u/a if, for you, the candidates can be divided into two sets such that the merit differences within each set are negligible in comparison to the merit difference between the sets.

Good, we are making progress. Term "u/a" now has a definition "if, for you, the candidates can be divided into two sets such that the merit differences within each set are negligible in comparison to the merit difference between the sets". Terms "acceptable" and "unacceptable" refer to this definition of "u/a".

> Also terms "compromise"
>  
> [endquote]
>  
> I refer Juho to a dictionary, if he wants to find out what “compromise” means.

It seems to be just a chosen name for the "only acceptable who can beat the unacceptables". It seems that the strategy has a condition that there must be exactly one acceptable candidate that is also a potential winner (for he precondition for the use of the strategy to be true).

> As I’ve been saying, of the two sets referred to in the above-stated definition, the “acceptable set” is the one that the voter in question prefers to the other set. That other set is the “unacceptable set”. An acceptable candidate is a candidate in the acceptable set. An unacceptable candidate is a candidate in the unacceptable set.

We seem to have the same definition.

> he’s taken on a new tactic, one of asking for definitions

The reason why I (systematically) request exact and directly implementable definitions is that in order to have a strategy that would work in real life elections we must have a definition that we can print in the newspapers and then expect regular voters to follow. (An alternative would be to have a strategy that we can send to the parties and other interest groups, and based on that description those groups could then publicly recommend how the voters should modify their vote, or what kind of a vote to cast.)

In the EM disdussions we often talk about and try to prove the existence of a modified vote set that would change the winner to the benefit of the voters whose votes were modified. The existence of such modified set of votes I have called "theoretical vulnerability". When we want to comment the viability of different election methods in typical real life elections we should talk about "practical vulnerabilities" or "practical strategies" that can be implemented systematically in a successful way in the targeted societies, with incomplete information about the opinions, just guesses of the votes that will be cast on the election day, with incomplete ability to steer the voters to follow the various possibly simultaneous and alternative strategies, and with other interests of the voters like interest to show support to their favourites even when they can not win, maybe in preparetion for the next elections. ("Practical strategies" could be given also a more formal definition, but maybe that is good enough to be used softly in the less than mathematically hard real world.)

Then back to the strategy.

An alternative definition of the strategy could be "If, for you, the candidates can be divided into two sets ("acceptables" and "unacceptables") such that the merit differences within each set are negligible in comparison to the merit difference between the sets, and there is exactly one acceptable candidate that can win all the unacceptable candidates, then you should rank that acceptable candidate first and then rank all the other candidates in your sincere preference order".

For example a voter with sincere opinon a > B > c >>> d > e should vote B > a > c > d > e. The uppercase letter refers to the candidate that, according to the voter, can win all the unacceptable candidates. The strategy does not take position on if there are potential winners among the unacceptable candidates.

Btw, the conditions of the strategy could maybe be also a bit more relaxed with respect to candidates than the voter expects not to win in any case falling exactly in the "acceptable" and "unacceptable" categories. I mean that maybe it is enough if all the other potential winners are unacceptable, for the strategy to take effect. But this is a minor topic that we can skip for now. Also the case where there are no unacceptable potential winners could be slightly different.

The strategy says that if the top favourites of the voter are candidates that can not win, then they should be buried under the only acceptable candidate that can win (the "Compromise") (if such a candidate exists). The key strategic thought behind the strategy must be that by burying those candidates as a precaution they can not be used to (or accidentally) bury the only acceptable potential winner. If so, then this is a defensive startegy whose idea is to respond to another offensive strategy used by others (or maybe as a very marginal case, a response to an unintentional loop).

The strategy that this strategy responses to could be either rational or irrational. If it is a rational strategy, then there should be another description of that rational strategy for voters to follow. Alternatively one could assume that large number of voters will have a tendency to bury the "Compromise" under some minor candidates (including some of the favourites of this voter).

I assume that the strategy applies at least to all typical winning votes based Condorcet methods.

Am I on the correct track so far?

Juho



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