# Majority Rule Standard

Steve Eppley seppley at alumni.caltech.edu
Tue Nov 19 12:17:18 PST 1996

```Hugh T wrote:
>Mike Ossipoff frequently writes:
>>If a full majority of all the voters indicate that they'd rather
>>have A than B, then, if we choose A or B, it should be A.
>
>I think I understand what is meant, but I also believe it could be
>expressed more precisely.  In particular, how is "voters" defined?
>It could mean
>  (a) registered voters
>  (b) those who vote in any election that is on the same ballot
>      with the A vs. B race
>  (c) those who vote in any pairwise race on that ballot for the
>      office for which A and B are contending
>  (d) those who vote in the race A vs. B.
>I believe (c) is intended, but "all" might make a case for (b), if
>not (a).

Yes, c is closest but c is a mangling of the meaning.  Voters don't
explicitly vote in separate pairwise races when they rank the candidates
(e) those who rank any candidates for the office.
Clear enough?

>I am not sure what "full" adds to the statement.

Neither am I.

>I admit that the version with definition (c), as a standard
>independent of that with definition (d), does not strike me as an
>intuitively compelling standard.

I find it compelling.  When there's only one candidate whose election
would not violate that principle, what case can be made for electing
someone else?

If there are no candidates whose election would not violate it, then
you can fall back on a slightly more relaxed principle, like electing
the candidate which would minimize the number of voters who would
prefer another.  In my view, this is the key principle.  The
beats_all winner--if there is one--and the candidate for whom no
"full" majority prefers another--if there is one--are cases which
are both covered by this principle.  (Condorcet does better than
Smith//Condorcet on this principle, but I'm willing to accept
Smith//Condorcet over Condorcet because the Smith criterion is
important for so many academics and I don't want them to oppose
sw reform.)

>If both versions appear to be violated in an election (due to a
>Condorcet circular tie),

I'd prefer we not refer to circular ties as "Condorcet circular
ties."  It may be nice to credit the Marquis with their discovery,
but in a discussion of Condorcet's method it can give the impression
that they're part of the method.

More important, it's not true that when there's a circular tie there
can't be a candidate whose election wouldn't violate versions (c) and
(e).  If there is one, elect this one.  Why elect a different one?

>                         I won't feel much better about it just
>because enough absentee ballots turn up that express no preference
>between A and B to reduce A below a "full majority" under (c).
>Should I feel relieved in that case, more than if those absentees
>had not bothered to vote in the race at all?

Wrong question, I think.  Would you feel more relieved if some other
candidate is elected, and if so, why?

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```