On 25.5.2012, at 0.17, Michael Ossipoff wrote:
> Juho says:
>
> 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).
>
> [endquote]
>
> Wrong. There need only be one or more possibly-winnable candidates in each of
> the two sets, in order for it to satisfy my definition of u/a.
Based on what you say "u/a election" could be redefined => "if, for you, the
POSSIBLY-WINNABLE candidates can be divided into two (NON-EMPTY) sets such that
the merit differences within each set are negligible in comparison to the merit
difference between the sets".
In my comment I however referred to the definition "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". Words "the only acceptable" refer to exactly
one possibly-winnable acceptable candidate. Later on in your mail you said that
this limitation is not necessary, so let's assume also that limitation it's
gone now.
> 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".
>
> [endquote]
>
> Your “alternative definition” is the same as the definition that I’d been
> giving, except for the sincere preference order of the other acceptables. I’d
> merely spoken of the need to rank Compromise alone in 1st place. I don’t
> necessarily agree about the “sincere preference order” for the other
> acceptables. If they can’t win, why would it make any difference. If they
> have some small chance of winning, then it would seem best to rank them in
> order of what winnability they have.
Ok. I picked the sincere rankings from the air as a default answer since their
treatment was not defined. If the voter rearranges those candidates he probably
does so because of some other strategy or other needs that are not part of this
strategy. So I guess the default behaviour is still sincerity but we don't want
to require it.
> And it really maybe needn’t be that Compromise is the only candidate that can
> beat Worst. I said it that way for simplicity. It’s probably enough that
> Compromise has a better chance than the other acceptables. I haven’t given
> consideration to that, because I’ve preferred the simpler case in which
> Compromise is the only candidate who can beat Worse.
Ok. It seems that Compromise is the one of the possibly-winnable acceptable
candidates that has highest chances to win (according to the voter), and only
that candidate will be ranked alone in 1st place. This means that the ranking
of the other possibly-winnable acceptable candidates is not defined.
(I note that ranking your second best possibly-winnable acceptable candidate
above your best possibly-winnable acceptable candidate may also make the
outcome of the election worse.)
> Later I said that it needn’t be u/a. The important thing is that Compromise
> is the only candidate who can beat Worse.
Ok. The strategy should be defined without the u/a criterion. That would mean
giving up the requirement of strong merit differences between the acceptable
and unacceptable candidates.
> Favorite-burial only makes any sense if Worse, or the unacceptable, is/are
> winnable.
Ok. The strategy should be redefined so that at least one of the unacceptables
is winnable.
(I guess terms "Worst" and "Worse" that you use refer to some of the
unacceptable candidates.)
> As I was saying, I now don’t say that u/a is necessary for the optimality of
> favorite-burial in Condorcet.
I referred to the possibility that your strategy could be classified as a
defensive strategy that would be a reaction to some offensive strategy that is
used by some other voters (and only marginally against situations where votes
somehow unintentionally cause a burial like loop). You seem to recommend your
strategy as an optimal strategy that is beneficial in all situations (including
fully sincere elections as well as ones where other strategies are present). So
let's assume that.
> Juho says:
>
> I assume that the strategy applies at least to all typical winning votes
> based Condorcet methods.
>
> Am I on the correct track so far?
>
> [endauote]
>
> Yes, I’d say that, under the conditions I described, favorite-burial is
> optimal in all Condorcet(wv) versions. But the sometime optimality of
> favorite-burial is, by definition, a property of all FBC-failing methods. I’m
> not trying to single-out Condorcet(wv). It’s just one of many FBC-failing
> methods.
Yes, but note that I'm trying to see if the theoretical vulnerability
(="sometime optimality") can be made also a practical vulnerability in a real
election (="practical optimality").
And then back to the strategy definition.
I'm not 100% sure that my interpretation of your proposed changes are correct,
but here's one considerably simpler version that tries to take the proposed
modifications into account (including the idea to drop the u/a criterion's
strong merit difference requirement away, but keeping terms "acceptable and
"unacceptable", assuming that the voter can make that division also when the
merit differences are not radical).
"If you think that there are both acceptable and unacceptable candidates that
are possibly-winnable, then pick the one of the acceptable candidates that is
most likely to win all the unacceptable candidates, and rank that candidate
first before all the other candidates."
Is this in the direction that you wanted?
Juho
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