"Best" candidates, and Social Orderings (was: [EM] Sincere methods)

[Jobst Heitzig]

Dear Folks!

The following comment of Juho's made me think about the concepts of
"best canidate" and "Social Ordering" again.

Juho Laatu wrote:
> If the "god" that elects the best winner would be one
> individual, then we could expect him to give a linear order to the
> candidates. And in this case it looks natural that candidates outside
> the Smith set must be lower than candidates in the Smith set. And it
> looks natural that after this decision all that there is left is to
> break the loops in the Smith set and make also their order linear. But
> as we know, group opinions may contain natural cycles and one can not
> say that they are wrong and should be corrected. For this reason I find
> methods that try to e.g. evaluate each candidate separately more natural
> than ones that try to force the group preferences into some linearly
> ordered preferences.

Let us look a bit deeper at the notion of "best candidate":

First of all, the principal aim of a single winner election method is to
find a single winner (that's trivial). Intuitively, one is tempted to
say this should be "the best" candidate. But this implicitly assumes
that there *is* a "best" candidate. We know of course that most often
one can easily find two measures which do not agree on which candidate
is "best", so we're left with deciding which measure is most important.
But what if no measure is "most" important but each is important in some
sense or other? Then perhaps there is a most important sense in which
measures can be important... etc...

Some methods focus on one measure, for example Plurality (direct
support), Approval Voting (approval score), Copeland (number of pairwise
defeats), MinMax (strength of strongest defeat), Beatpath (strength of
beatpaths), Kemeny (using some measure of fit between a social order and
the pairwise defeats), ignoring all other measures.

Other methods consider more than one measure, for example DMC (approval
score and pairwise defeats) or DFC (approval score, pairwise defeats,
and direct support).

My claim is that the latter are much safer against arguments of using
the wrong measure when there is no agreement upon which measure is most
important.

So, I suggest not to claim your favourite method finds "the best"
candidate, as so many of us frequently do. Rather, one should say that
the favourite method elects a "very good candidate as measured by
<whatever>" and then explain why those measures are considered important!

DFC, for example, is my current favourite since it elects a very good
candidate as measured by direct support, approval score, and pairwise
defeats, and I find this combination of measures most satisfying since
they correspond to the three most basic complementary forms of
preference information:
1. Individual direct support, answering the "global" question of which
candidate I would personally elect if I could decide.
2. Approval, answering the "local" question of whether I find a
particular candidate acceptable or not.
3. Pairwise preferences, answering the elementary comparison question of
which candidate I would personally elect if only these particular two
were feasible.


Now, what about "social orderings"? Why should anybody want such a thing
or assume that such a thing should exist?

The implicit assumption behind a social ordering is not only that there
is a "best" candidate, but that there is even a "second best", "third
best", and so on. Why the hell should that be the case when there is not
even a clear notion of "best"?

Of course, a social ordering can be useful in some situations, for
example when it is not clear beforehand which of the options are
actually feasible, like when deciding upon the movie to watch without
knowing which movies might be sold out. But in an election, there is no
such uncertainty, and in the unlikely case in which the winner becomes
unavailable between the election and the time of taking office, one
would rather hold a new election than put the "2nd best" candidate in
office...

Another use of social orderings could be for information purposes: Which
candidates were "close to winning"? But such questions can easily be
answered independently after the actual election, for example by
reporting how many voters would have had to vote differently to get the
particular candidate. But there is no reason why the latter measure
should be involved in *finding* the winner in the first place. Likewise,
one can report after the election on the strongest beatpaths from the
winner to all other cnadidates, without any need to consider beatpaths
for finding the winner. Actually, I think one should report as much and
as diverse information as possible to justify the winner once s/he is
determined, no matter whether that information was used in finding the
winner.

Finally, there is an important criterion by Steve, "immunity from 2nd
place complaints", which seems to indicate that a social ordering was
needed. But that criterion only states that when we remove the original
winner and apply the method *again* after striking out that candidate
from all ballots, then the new winner should not be one who defeats the
original one pairwise. This is a useful criterion, but it has nothing to
do with social orderings, at least in my opinion.


So, I suggest we should drop the idea of "social ordering" altogether
and never mention it to anyone, especially not when arguing in favour of
some single winner election method, because it is absolutely misleading.

Yours, Jobst