# Pairwise Show-Of-Hands Voting

Mike Ossipoff dfb at bbs.cruzio.com
Fri Dec 6 01:35:09 PST 1996

```You wouldn't want to use Condorcet's method in show-of-hands
voting, where you separately vote between pairs, 1 pair at a time,
because the results of 1 pair could make it obvious to some voters
that they have a win via order-reversal cheating. But a slightly
refined Condorcet would be used for show-of hands, and a simpler
pairwise method could be used. Both of these 2 pairwise methods
suitable for show-of-hands are methods that could use
2 ballotings:

BeatsAll//Approval (also called Runoff-Pairwise):

Conduct pairwise voting by show of hands, voting between pairs
of alternatives 1 pair at a time. If one alternative beats everything
it wins. Otherwise conduct an Approval vote between all the
alternatives.

Smith//Approval:

Same as above, but if there's no beats-all winner, the Approval
vote includes only the alternatives in the Smith set (the
circular tie).

Condorcet///Approval:

Conduct pairwise voting by show-of-hands, as before, doing 1
pair at a time. If 1 alternative beats everything else it wins.
If not, then use Condorcet(EM)'s choice rule:

The winner is the alternative with fewest votes against it
in a defeat.

But: If every alternative has an alternative voted over it
by a full majority of all the voters, then hold an Approval
vote among all the alternatives.

Smith//Condorcet///Approval:

As above, except that Condorcet's choice rule is used among
the Smith set (circular tie), the condition requiring the
Approval vote is that every Smith set member has another
alternative voted over it by a majority of all the voters,
and, if Approval is used, it's only used among the Smith
set.

***

I should define the Smith set:

The Smith set is the smallest set of alternatives such that
every alternative in the set beats every alternative outside
the set.

***

In all these 2-ballotng pairwise methods, the results of the
pairwise voting will give very good information for use in
the Approval vote, if an Approval vote is required. In
that Approval vote it will be obvious how far, if at all
a voter needs to compromise in that vote.

***

By the way, I never did write explicit instructions for
repeated balloting with Approval:

Conduct Approval votes until either 1 or more alternatives
have a vote total equal to at least 1/2 the number of voterss,
or till there have been N-1 ballotings (N = the number of alternatives),
whichever happens 1st. At that time the alternative with the most

***

Repeated Balloting with Approval is my suggestion for when
there's time to do N-1 Approval ballotings, but there
isn't time to do pairwise voting.

***

Mike Ossipoff

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