# [EM] A solution for incomplete preference orders

mrouse1 at mrouse.com mrouse1 at mrouse.com
Sat Jan 6 08:39:19 PST 2007

```Many vote aggregation methods have a problem with bullet voting, truncated
ballots, and multiple candidates ranked the same on a single ballot. A
voter should not obtain a better result by *not* showing a preference, but
neither should the ballot be ignored if the voter cannot give a *complete*
preference.

One partial solution is to require all candidates for an office give a
complete preference order before the election, which will also be
indicated on the ballot itself. This ranking would be used to complete all
ballots without a full preference order.

Let's say candidate A picks the order A>C>D>B. If a person votes for
candidate A and ranks no one else, the vote will read A>C>D>B. If another
person votes A>D and no one else, the ballot will be read as A>D>C>B.
Ballots with A>B=D (where B and D are tied on a ballot) will have B and C
placed in the same order as on A's ballot, or A>D>B>C.

This is only a partial solution, since it's possible that someone will
rank two or more candidates at the top, making it more difficult to figure
out the best preference order for the remaining candidates (though you can
pair up ballots -- if two people say A=C, you can have one A>C and one C>A
-- though this could still leave some equal top preferences).

It need not violate the candidates' right for a secret ballot, since they
can still vote whatever order they want on their own ballot (though it
would be rather silly to do so). Since candidates are expected to have
public votes for their entire term of office, this is a minor point, and
knowing how each candidate views his opponents in the race would be
important information for voters.

I'd be interested in any arguments against or suggestions for this (and
other) preference-filling options.

Michael Rouse

```