[EM] "Unmanipulable Majority" strategy criterion

[Abd ul-Rahman Lomax]

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.