On Jan 4, 2005, at 11:09 PM, James Green-Armytage wrote:
Range voting is neither a majority rule method, a supermajority rule method, nor a proportional representation method. Therefore, its applications are very limited.
Let's say that our voting scenario is a large group of people choosing an
executive (e.g. a mayor or president), and there is enough at stake that
people cannot be relied upon to vote sincerely.
I don't think that range voting should be used for this scenario. Why not?
Because it is not a majority rule system. It is possible for a candidate
to win in range voting even if they are the last choice of 99% of the
voters. Unlikely, but mathematically true.
Since you are talking about an election method that indeed should not be used, who here has proposed using such a method? I expect that the method you are striking down is subtly but crucially different than anything anyone was actually promoting.
So, the example in that last paragraph looks something like this, right? 99* 1.0, 0.0 1* 0.0, 100000000.0
But I don't remember any suggestions that we have such unbounded ballots and straight rating summation.
There has been some talk of maximizing social utility, some of it mine, and if the above example represents a true measure of utility, then it poses an interesting ethical and philosophical puzzle. Early in his often cited book, Kenneth Arrow asserted that you can't measure interpersonal utility. That's why he focused on orderings, personal and social. I disagree and say that we implicitly do measure interpersonal utility by giving everyone "one vote" and thus we give everyone equal utility and an equal share of the social utility.
To that end "cumulative" and "normalized" forms of ratings exist.
Of course, even a 1-100 scale can be so "abused". But if 99 people really vote for their favorite with a "1", and the other guy with a "0", aren't they effectively saying "I don't care (much)"? Why should we be listening to their votes more than they want to be heard?
In contentious executive elections, I think that we should stick to
majority rule methods. What is my operational definition of majority rule?
The winner should be a member of the minimal dominant set (aka GeTChA or
Smith). A weaker definition would be the mutual majority criterion. Range
voting passes neither of these criteria, and so I say it has no claim on
being a majority rule method.
Ah, but a different definition of "majority rule" can most naturally be expressed on a rated ballot. The Rule that says a majority of the people think that one of the choices is worth having at all. On a positive/negative rating scale ballot, a winner must have a positive average rating. If no choice achieves this, disqualify them all and run a new election.
Is it somehow better than majority rule? In some non-contentious election
scenarios, perhaps it can be. But in a contentious election, it is not. If
a Condorcet winner is not elected, it does not necessarily mean that
another candidate had a higher utility. More likely, it means that
supporters of the other candidate pulled off a successful strategy. The
interpersonal utility comparison aspect of range voting is just too easy
to hijack for strategic purposes, so that it essentially becomes
meaningless in a contentious election.
I think you should justify that more in the face of something other than free-range voting.
If one is concerned about the tyranny of the majority, range voting is not
the answer, because a well-coordinated majority can still guarantee
victory for their candidate of choice. If one is concerned about the
tyranny of the majority, one should look at supermajority methods and
proportional representation methods, rather than at pseudomajority methods
like range voting, approval voting, and Borda.
I guess it's still a question of what we're measuring to find "majority". Any election method finds the choice with the _most_ of some quality. That quality comes through various methods from the voters. I guess I'm asking for clarification on what exactly it is about the process of these other methods that you don't like. For example, I have a negative gut reaction to any non-deterministic method and I'll back it up with rhetoric like "people should vote, not random number generators".
Brian Olson http://bolson.org/
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