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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