[EM] Are proposed methods asymptotically aproaching some limit ofutility?
mikeo2106 at msn.com
Sun Mar 11 12:59:54 PDT 2007
Matthew Welland wrote:
there is an academic
>path and a pragmatic path.
Dont fall into the Democrat trap of believing that pragmatic has to be
less than really good. MDDA is extremely simple, briefly-defined. And yet it
has a very impressive list of criterion-compliances. MAMPO is even better,
though not quite as simple (but still as simple as IRV).
MDDAs definition is so brief that I might as well repeat it here:
Voters may rank, in order of preference, as many candidates as they want to.
Equal ranking permitted.
1. Disqualify every candidate over whom another candidate is ranked by a
majority (unless that would disqualify all the candidates).
2. Among the un-disqualified candidates, elect the candidate who is ranked
by the most voters.
[end of MDDA definition]
MDDA meets SFC, SDSC, and FBC.
>I want to know what to advocate in various
>forums and what to implement on my own web site.
It depends on how much definition-brevity your audience insists on, and
whether you want deluxe rank-method properties.
If simplicity isnt important, then I suggest SSD. Maybe, instead,
BeatpathWinner for website poll-counting or organizational use--as a
small-electorate substitute for SSD.
If simplicity and brief definition are important, but you still want
rank-method advantages, then use &/or propose MDDA, or maybe MAMPO, if
youre willing to give up a little simplicity.
If simple, obvious and natural motivation and justification are important, I
agree that a point-rating method is best. Of those, Approval is the best,
with -1,0,1 a close second. The advantage of these is that there are so many
ways to count rankings, that someone could always say, But why _that_
rank-count? With point ratings, theres only one way people expect it to be
counted: Add it up.
Dont use a point rating method with more than 3 rating levels. Theyre much
more difficult to vote than rankings or the 2 or 3 level point rating
systems. And, as others have pointed out, theyre very vulnerable to
strategists taking advantage of sincere voters. Every one of the 3 people
who have replied so far to your post have warned about that problem.
It even could exist to a degree in -1,0,1 which is one reason why Approval
is the best. With Approval, theres little or no difference between a
sincere ballot and a strategic ballot.
If you propose Approval, dont introduce it by saying you can vote for as
many as you want to.. That triggers confusion. Start by offering a -1,1
point rating system. You can give to each candidate a positive or a
negative. Then point out that you can halve the counting work if you count
only the positive ratings. And you can halve the voting work if you vote
only the positive ratings. So this method is equivalent to just marking the
better candidates and not marking the rest. The equivalence to -1,1 shows
that, in Approval, giving someone a low rating (such as no vote) is just as
powerful as giving him/her a high rating (a vote), because the low rating
that you give him/her cancels out the high rating that someone else gave
I mention that because if you dont deal with it, it will be a big problem
to most people, who will say What about 1-person-1-vote. Doesnt the person
who votes for more have more power? No, for the reasons I gave.
The appeal advantage of -1,0,1 over Approval is that people would enjoy
voting negative ratings. And, with 3 rating levels, a negative rating
carries more signficance. Of course just offering -1,1 would give people the
satisfaction of giving negative ratings, with all the advantages that go
with Approval, since its equivalent toi Approval. Maybe, as a practical
matter, -1,1 would be the best proposal of all.
You spoke of satisfaction. If (as I would) people vote for the acceptable
candidates in Approval, and not for the unacceptable, then Approval
maximizes the number of people who consider the winner acceptable.
If voting strategy is based on winnability and tie-probability
considerations too, then its been shown that, with a few reasonable
approximations, Approval maximizes the number of voters who are pleasantly
surprised by the outcome.
In Approval, the pair-wise preferences that we vote are the stronger,
emphatic preferences. Approval then can be said to elect the CW of emphatic
preferences. The Borda winner too. With just two preference levels voted,
theyre the same.
Of course, looking at it as ratings of the individual candidates, Approval
elects the candidate who is, overall, the most highly rated.
Approval can be regarded as voting one set of candidates over the remaining
candidates. Dividing the candidates into two sets and voting one set over
the other. You have the freedom to choose that favored set as you want to,
as large or small as you want to. The reason to vote for more than one is
for compromise. So one votes ones compromise set.
Compromise is an unavoidable part of 1-vote Plurality, though it isnt
acknowledged or allowed for in 1-vote Plurality, which assumes that you vote
for your favorite even though millions of people vote instead for a
compromise, then not even being allowed to rate their favorite above bottom.
Approval, Set-Voting, lets _you_ choose the size of your compromise set.
One can extend ones compromise set as far as one wants to. Maybe youre
only willing to compromise so far. Or maybe you compromise as far as you
believe that you need to. The beauty of Approval is that you can do it
either way. In fact you can vote according to any of the models or ways of
looking at it that Ive described here, and probably others too. How much
your voting options increase just by that one change from 1-vote
Pluralitiy!--adding the freedom of rating all the candidates as _you_ want
to instead of inexplicably being forced to give bottom rating to all but one
In addition to being able to compromise as far as you choose to, being able
to vote for a set of compromises makes it easier for diverse groups to come
together on a compromise. They neednt guess what compromise the others will
use. Just vote for all the acceptable candidates. It can be said that with
Approval you dont have to choose. The count will choose based on what is
acceptable to each voter.
Approval is the minimal change from the currently-used 1-vote Plurality. And
Approval is the minimal good method. And for that reason, Approval is also
the most obvious and natural good method.
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