# Continued: Voting Methods

Mike Ossipoff dfb at bbs.cruzio.com
Thu Oct 17 00:39:52 PDT 1996

```Topics replied to in this letter:

1. Ways of wording Condorcet(EM) definition
2. Equal preferences
3. Open meetings
4. The Smith set stops short of Copeland's problem
5. Iterated Condorcet & Stepwise Condorcet

***

1. Ways of wording Condorcet(EM) definition:

Here are some other wordings that have been suggested. Each
letter in the list represents a different wording:

a) The winner is the alternative with fewest votes against
it in a pairwise defeat by another alternative.

b) The winner is the alternative whose greatest defeat
by another alternative is the least, as measured bg how many
voters have ranked the defeating alternative over it.

c) For each alternative, determine which alternative that beats
it is ranked over it by the most voters. The number of voters
ranking that other alternative over it is the measure of how
beaten it is. The winner is the alternative least beaten by
that measure.

2. Equal preferences:

What I'd meant about that was that MPV (also known as Preferential
Voting, the Alternative Vote, Hare's method, the Elimination system,
& Instant Runoff) would have its problem someewhat mitigated, but
not eliminated by counting equally-ranked alternatives as all
having the full status of the rank that they share.

This was intended as a compromise between MPV advocates &
Approval advocates, but neither accepted it. That's ok, because
I prefer just using a better method anyway.

Of course this isn't an issue in Condorcet's method. If I
vote:

1. A
2. B & C & D
3. E

...that's counted as a vote for A over everything, a vote for
B, C, & D over E, and a vote for all those over everything not
ranked.

3. Open meetings with show-of-hands voting:

As Steve pointed out, one wouldn't want to use Condorcet or
Smith//Condorcet in a show-of-hands vote, because voters could
take advantage of other voters whose voting they've observed
in previous pairwise comparisons.

But there's a modification that can solve that problem.

First, though, the way such a method would be conducted, as somene
pointed out, would be to hold separate 2-alternative elections
between each possible pair of alternatives. Of course if the
initial pairs are well-chosen, it wouldn't be necessary to vote
between very many pairs to determine that something beats everything
else. Maximum # of pairs = N(N-1)/2, where there are N alternatives,
but it should rarely be necessary to actually vote that many.

Here's the Condorcet modifiction for show-of-hands:

Condorcet///Approval:

Use Condorcet's method, but if every alternative has another
alternative ranked over it by a full majority, then hold a 2nd
balloting between all the alternatives, using the Approval
method (the non-ranked method where voters may vote for as
many alternatives as they wish, giving each a whole vote).

Any attempt to take advantage of other voters would take the
form of "order-reversal", and a potentially successful order-reversal
would trigger the 2nd balloting, thereby gaining nothing for the
order-reversers. The pairwise results from previous voting would make
it quite obvious how far, if at all, a voter need compromise in the
2nd balloting. And it would leave the order-reverss in the spotlight
holding the bag.

In fact, Condorcet///Approval would also be good for public
political elections, with their secret ballots, if voters are
very sophisticated & devious, unlike existing electorates.

***

For show-of-hands, or paper-ballot, voting, in meetings or
committees where people agree on pairwise-count, but don't agree
on what to do when no 1 alternative beats each one  of the others,
I suggest BeatsAll//Approval, which has also been called
"Runoff-Pairwise":

With paper ballots, or with separate pairwise show-of-hands votes,
search for an alternative that beats each one of the others. If
one exists, it wins. If not, then hold a 2nd balloting between
all the alternatives, by Approval. A 2nd balloting is the obvious
circular tie solution when there's no agreement on one, or when
there isn't time to define, explain & advocate Condorcet///Approval.

***

Meaning of "///" & "//":

X//Y means: Use Y to choose from the alternatives that X has
narrowed the choices down to.

X///Y means: Use X. But if every alternative from the set from which
X is to choose has another alternative ranked over it by a full majority,
then use Y to choose from that set from which X was to choose.

The only "///" method I propose is Condorcet///Approval, and of
course Smith//Condorcet///Approval. As I said, in both methods
Approval is used in a 2nd balloting when it's used.

***

What to do when there's no computer (or no willingness to use one)
and it's necessary to do show-of-hands voting with too many
alternatives, too many voters, & too little time for a pairwise
count?:

Majority//Approval:

Ask people to vote for their favorite. If an alternative gets a
majority then it wins. If not, hold a 2nd balloting, by Approval,
between all the alternatives.

Approval-Majority//Approval:

Hold an initial Approval election. If 1 or more alternatives get
votes equal in number to half the number of voters, then the one
with most votes wins. If not, the hold a 2nd balloting by Aproval.

***

Majority//Approval is good for when there's a 1-dimensional issue
spectrum, because the results of the 1st balloting give a very
good indication of winnability, and of how far a voter must
compromise in the 2nd balloting.

Without a 1-dimensional issue-spectrum, that doesn't hold, and
Approval-Majority//Approval is better, because at least then the
1st balloting gives a good indication of how well alternatives
can do in an Approval election, information useful in the
2nd balloting.

***

Both these methods are versions of what could be called
"Inclusive 2nd Ballot".

***

Sure, especially if a group doesn't have an established
multi-alternative single-winner method, it might be tempting
to hope for y/n issues instead of multi-alternative ones.
That's the case in EM when dealing with opposition to
a proposal, if that opposition necessitates a vote: It's
nice if there are just 2 alternatives, such as "do it" or
"don't do it". But any effort to artificially put a
multi-alternative choice in the form of a structure of
and unfairness. It's a general rule that any time there are
more than 2 alternatives possible, including the "status
quo" alternative, there should be a single multi-alternative
vote rather than some combination of 2-alternative votes.

***

4. The Smith set stops short of Copeland's problem:

As Steve pointed out, though it's convenient to count victories
or defeats in calculating the Smith set, that's just done for
the purpose of determining that set of alternatives that all beat
everything outside the set. Where Copeland goes wrong is when it
uses victory & defeat counting to choose from within the Smith
set.

Did I talk about the reason for the Smith set yet? In case I
didn't, it assures that Condorcet's method will comply with
all of the academic criteria that I've heard of. Some of us,
including me, don't believe that's particularly important, but
proponents may not be able to afford to answer on an equal scale.
I feel that the _important_ properties of Smith//Condorcet are

***

5. Iterative Condorcet & Stepwise Condorcet:

Steve has already defined Iterative Condorcet, so I won't
repeat that here.

Stepwise Condorcet:

Each ranking is initially considered to include only its 1st choice.
If your 1st choice didn't win in the 1st round, then in the 2nd
in the 2nd round then in the 3rd round your ranking includes your
3rd choice. Etc.

This continues as long as the previous paragraph keeps causing
rankings to include next choices. The winner of the last round
is the winner of the election.

***

I consdider Iterative Condorcet better than ordinary Condorcet,
but its added complication can be justified only with sophisticated
devious electorates, without which ordinary Condorcet can't have
any problem. Likewise for Stepwise Condorcet.

I prefer Stepwise Condorcet to Iterative Condorcet because
Stepwise Condorcet accomplishes something similar without ever
promoting anything but one's favorite to 1st place. Stepwise
Condorcet works because of Condorcet's ability, even when sophisticated
devious voting is attemped, for voters to defeat an alternative
with a majority against it merely by not including it in their
rankings.

***

Mike Ossipoff

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