[EM] Simmons' "solution" of voting system design puzzle is inadequate

[Abd ul-Rahman Lomax]

At 05:00 PM 1/20/2007, Chris Benham wrote:

>By this definition Range fails "ICC" because voters can only express
>preferences among clones by not giving maximum possible score to all of
>them, thus making it
>possible that if a narrow winner is replaced by a set of clones all the
>clones lose.

Now, tell me, why should an election system provide a means for 
voters to express a preference between clones, when they consider 
them equally fit for the office?

Benham is correct that Range would not allow a voter to express a max 
score to one candidate and a lower score to another, without risking 
the loss of the second one as he described. If a voter considers two 
candidates clones, the rational vote under Range is to rate them 
identically. "Favorite", between clones, is meaningless. If the voter 
has a preference, they aren't clones to the voter.

I've been finding this kind of dual perspective, one might call it 
inconsistency, quite common in Benham's writing. A clone is, by 
definition, functionally identical to the voters. There are voting 
systems where the existence of clones alters the outcome of the 
election, and we intuit that this is undesirable. Range should not. 
By definition, if the voters consider two candidates clones, they 
will rate them identically, otherwise we have no basis for calling them clones.

What Range encourages is honest voting. Changing your rating of a 
candidate, not giving the candidate your sincere rating, because you 
want to affect the election outcome (to elect one clone over 
another), is strategic voting. And in this case, there is no rational 
motive for it. To say it again, if you prefer one clone to another, 
they are not clones for you. Otherwise, what in the Sam Hill is a clone?

Okay, so I looked up "clone." It has a special meaning; the term was 
invented to apply to ranked methods. According to the current 
Wikipedia article on Strategic Nomination:

>Clones in this context are candidates such that every voter ranks 
>them the same relative to every other candidate, i.e. two clones of 
>each other are never both strictly separated by a third member in 
>the preference ranking of any voter, unless that member is also a fellow clone.

Because of this definition, it is possible that all voters would rank 
two candidates the same, but would sincerely rate them differently, 
if the resolution of the Range method were sufficient. It is not 
immediately obvious to me that Benham's contention, given this 
definition, is true, but I also can't affirm that it is false.

But the *intuition* behind the idea of ICC is that the introduction 
of identical candidates should not affect the outcome. Identical was 
then defined within the context of ranked ballots. Range provides 
more information about voter preferences than do ranked ballots, and 
it seems possible that this additional information, which *is* used 
by Range, could result in the loss of both clones, but only if (1) 
the election was very close -- as Benham noted -- and voters lower a 
candidate's rating in order to elect another. That is, if candidate 
A, their favorite, was previously rated at 100, and the voter prefers 
B, whom they would also rate at 100, and they thus lower their rating 
of A to 99, A could as a result lose. Because the voter has chosen to 
alter his or her vote strategically. The problem arises because of 
normalization, it seems.

The relative ratings of candidates should not be affected by the 
introduction of clones, but if one is introducing a new clone at the 
extreme, the favorite of some voters, it could nudge down the vote of 
their previous favorites if they normalize. Normalization causes 
Range Votes to shift, even when they are sincere. (Normalization is 
the process of voting full strength by rating at least one candidate 
at 100% and at least one at 0%.) I would say that the voter should 
rationally "make room" for the new candidate by lowering the score of 
all other candidates by one point, which would probably deal with the 
problem, but there would remain the situation of the other candidate 
being already zero before the introduction of the clone.

The scenario, this last one, seems extraordinarily improbable to me, 
i.e., that the zero-rated candidate would be napping at the heels of 
the otherwise winner, but I suspect that scenarios could be contrived 
to show it.

Note that if two candidates are so close to each other that a slight 
lowering of the ratings (by the minimum resolution of the Range 
implementation) shifts the election, the utility of the two 
candidates is quite close, and, in Range 100, below the level of 
reasonable judgement of difference. It is down in the noise. And thus 
extremely little harm is done, even if it does technically fail ICC.

The habit of judging election methods by a set of intuitive criteria 
is actually a bad habit. If a method selects the winner who is best 
for the society, however we define it, do we care if it satisfies 
this or that criterion? What we need is a standard for judging the 
effectiveness of an election method, that is, the *result*, and the 
criteria that are normally considered don't do that. They focus 
instead, on certain characteristics, presuming that such a candidate, 
given certain conditions, should win. But the conditions are not 
necessarily related to the utility of the winner to society.

The criteria were, nearly all of them, developed to compare ranked 
methods, and thus they assume a ranked method to make full sense of 
them. Range could be called a ranked method, but if you do that, you 
must assume a continuous space of candidates, a virtual universe of 
candidates, such that all ratings are occupied for all voters and 
that an exact rating is available for every candidate. The failure to 
satisfy ICC can then be seen as an artifact of Range resolution and 
normalization.

If we don't agree on how to measure the worth of an election of a 
particular candidate, we won't agree on the best election method, 
i.e., how to get there most reliably.

And the only method I've seen proposed for measuring the accuracy of 
election methods at reaching that goal, the goal of finding the best 
candidate, is in the work of Warren Smith, which led to Range Voting. 
Range Voting *is*, if voters are sincere in their ratings, a method 
of measuring the utility of the election of each candidate, and it 
chooses the candidate with the highest total expressed utility. (At 
least, sum-of-range does that, average Range finds the highest 
average utility and introduces certain special problems.)

It is quite arguable, so far, that Range would not function this way 
in actual practice, because of strategic voting, but Range would 
still remain as a method of comparing election methods. How often 
does the method choose the Range winner, if the voters vote 
sincerely? A Range ballot can be an expression of voter preferences, 
including preference strength information directly, rather than 
imputed from ranks, which is problematic. Call it the Range Criterion.

And most methods would sometimes fail to select the sincere Range 
winner. (Range may also fail to select that winner if the resolution 
is inadequate, but, if it does fail, it fails gracefully, by electing 
someone who is almost indistinguishably acceptable.)

Because 100 steps of rating are probably down in the noise when it 
comes to human ability to meaningfully rate (10 steps is considered 
difficult), it should be more than adequate. We have argued that 
Range 10 or 11 would be enough. The possible reduction in the 
election value would still be quite low, and quite possibly below the 
social cost in ballot complexity for the higher resolution Range.