# [EM] "Unmanipulable Majority" strategy criterion

Abd ul-Rahman Lomax abd at lomaxdesign.com
Tue Dec 2 13:47:54 PST 2008

At 01:21 PM 11/26/2008, Chris Benham wrote:
>I have a suggestion for a new strategy criterion I might call
>"Unmanipulable Majority".
>
>*If (assuming there are more than two candidates) the ballot
>rules don't constrain voters to expressing fewer than three
>preference-levels, and A wins being voted above B on more
>than half the ballots, then it must not be possible to make B
>the winner by altering any of the ballots on which B is voted
>above A.*
>Does anyone else think that this is highly desirable?

Compared to what?

Chris, you know I have a high level of suspicion about all the
"election criteria," though monotonicity seems pretty basic, I mean
it is highly offensive to me that one could cause a candidate to lose
by voting for the candidate.

The Majority Criterion and the Condorcet Criterion, once consider
no-brainers, turn out to be quite defective, preventing an optimal
election outcome, i.e., there are situations, fairly easy to
describe, where all of us would agree that there was a better outcome
than the first preference of a majority or the pairwise winner. It
is, of course, a different question as to whether or not these
criteria are important for large public elections, but voting systems
theory is about *all* elections, not just public ones.

However, what are the implications of this criterion?

Here is what it does.

Range ballot, the only kind that can get around Arrow's Theorem (in
substance). The only kind that directly expresses preference
strength. I can modify the Range method to satisfy the criterion, but
it then becomes a non-deterministic method. WTF are we always wanting
a deterministic method, when this is the major stumbling block to
finding democratically ideal winners?

Anyway, let's just look at two candidates. There are others which
explain the range of votes, but we only need to look at two.

51: A 5, B 4
49: A 4, B 5

A is rated (equivalent to ranked) above B on a majority of ballots.
Alter the 49% to

49: A 0, B 10.

B wins, by a landslide, actually. Was this a better result than if A
continued to win?

Elections like this, with realistic examples behind them, are the
reason why the Majority Criterion, which this is a variation on, are
suspect. Let's assume that those ratings are sincere, in both cases.
In the first case A is, from the votes, a reasonable winner, but it
is close. In the second case, A is *not* a reasonable winner, and
there is a high likelihood that a majority of voters, in a real
runoff, would vote for B.

I've explained elsewhere why.

Allowing weak preferences to overcome strong preference is an obvious
error! It is *not* what we do in real deliberative process or in
making personal decisions, particularly in small groups.

Range does not satisfy the Majority Criterion, and no method which
considers and uses preference strength can, except by a trick.

In the election I described, because preference analysis shows that a
majority preferred a candidate other than the Range winner, I'd have
the election fail. Further process is necessary.

The common way is with a runoff election, where the top two are
listed on the ballot. There are possible variations on this; I have,
for example, proposed that the runoff between the Range winner and a
candidate who is preferred by a majority to the Range winner (if
there exist more than one such -- that should be extraordinarily rare
-- I'd make it be between the Range winner and the highest
sum-of-ratings Condorcet winner or member of the Smith set. I.e., I'd
use the ratings to resolve any Condorcet cycle.

These runoffs would be rare, usually Range chooses the Condorcet winner.

I have also argued that, usually, the Range winner would beat the
Condorcet winner in a real, delayed runoff, because of preference
strength considerations, which affect turnout and which also affect
how many voters change their minds. Have a weak preference -- which
is the situation here -- and it's more likely you will change your
mind. Both of these effects favor the Range winner. Only if the Range
results were distorted, perhaps by unwise strategic voting, would the
Condorcet winner prevail.

This trick turns the overall method into one which satisfies the
Majority Criterion, because that criterion applies, properly, to the
runoff. The first election, really, failed. But it guided ballot
placement in the second, perhaps, and the majority favorite was
guaranteed position on that ballot. All the majority has to do is
persist a little. But they will usually, in a healthy society, I'd
submit, step aside. They will collectively say, well, if you want
that outcome so badly, be our guest. I'm sure you will return the
favor someday.

And that is how real elections in real societies that value unity and
cooperation actually work. Fortunately, the world doesn't run only by
the kind of political division and confrontation that we are accustomed to.