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- Path: sparky!uunet!gumby!destroyer!cs.ubc.ca!fs1.ee.ubc.ca!jmorriso
- From: jmorriso@ee.ubc.ca (John Paul Morrison)
- Subject: Re: Voting Systems (was Re: Proportional representation)
- Message-ID: <1992Nov10.232346.16365@ee.ubc.ca>
- Organization: University of BC, Electrical Engineering
- References: <1dk6adINN5jb@iskut.ucs.ubc.ca> <1992Nov9.022817.20512@ee.ubc.ca> <1dncomINNapt@iskut.ucs.ubc.ca>
- Date: Tue, 10 Nov 1992 23:23:46 GMT
- Lines: 125
-
- In article <1dncomINNapt@iskut.ucs.ubc.ca> ramsay@unixg.ubc.ca (Keith Ramsay) writes:
- >It can apply, and I will explain again how it may be applied. In
- >order to apply it properly, you have to choose appropriate definitions
- >of the terms involved.
- >
-
- OK, this is where it gets more precise. I see what you mean.
-
- >In particular, you have to use the notion of "alternative" which is
- >"alternative", and then claimed Arrow's theorem *cannot* be applied,
- >because it can't be applied with your sense of "alternative"
- >substituted for the one to which the theorem naturally applies!
- >
- >Arrow's theorem applies to voting systems which can be described as
- >producing one of various "outcomes" or "alternatives", depending upon
- >the preferences of each of a group of voters. An outcome consists of a
- >complete description of the decision arrived at. If A and B are
- >distinct outcomes, then A and B are incompatible, since they both
- >give complete accounts of the result of the vote, and the accounts
- >differ from each other.
- >
- >As I wrote before:
- >|For this voting system the "alternatives" being chosen from, i.e., the
- >|possible outcomes of the vote, include all the possible ways of
- >|selecting a group of delegates, with weights assigned to them (which
- >|total up to the number of voters). It is clearly not allowed for
- >|voters to arrange all of these (zillions of) possibilities in priority
- >|order.
- >
- >For instance, suppose we have 10 voters, who are also the people
- >eligible for office. Then there are 92378 possible arrangements of the
- >resulting "parliament"- one for each choice of "weights" which add to
- >10. Each of these is an outcome which could occur in this system, if
- >we were all to vote in a certain way.
- >
- >A voter can have quite complex preferences among these alternatives.
- >Perhaps I am a voter who remembers the kind of mess we had after the
- >last election, when each of us voted for himself, and would like to
- >have a smaller number of representatives this time. It is conceivable
- >that *all* of us would rather have one certain arrangement, such as
- >{A has 3 votes, D has 4, H has 3} (since we regard A, D, and H as
- >being good, balanced representatives of our various opinions, likely
- >to produce results akin to what we'd produce ourselves), than have the
- >situation where each of us packs up and goes to parliament with his or
- >her own vote.
- >
- >One or two of the conditions mentioned in Arrow's result imply that in
- >such a case, the outcome will never be that each of us ends up with
- >just 1 vote in parliament-- since we all prefer the {A:3, D:4, H:3}
- >outcome. This is a condition which can easily be failed by this voting
- >system.
- >
-
- What I think you are trying to say (what Arrow is saying) is that even
- if we all want {A:3, D:4, H:3} there is no way to vote in a way that
- would gaurantee this, UNLESS we knew the outcome ahead of time.
-
- Since we can't knw how everyone else would vote, we don't know whether
- voting for A will help get you {A,D,H} = {3,4,3}, or in fact everyone
- might think that way, and we might get {A,D,H} = {10,0,0}, simply because
- we think D already has enough support to D=4.
-
- >It also does not express itself as directly as a function of the
- >voters' preferences among the available possible outcomes. Suppose I
- >happen to know precisely which compositions of parliament I prefer to
- >which other ones. It still may not be clear who I will vote for, in
- >order to get the composition I want most. Even if we all have written
- >down the 92378 possibilities in rank order, the system does not give
- >us a well-defined outcome. So it fails that (fairly basic) condition.
- >
-
- i.e. because you can't know how everyone else will vote, you don't know
- whether a vote towards A willl help get you {3,4,3} or actually
- gets you {10,0,0} (which you might not desire}
-
- It seems to me that Arrow implies that the only time you CAN know exactly
- which way to vote, is if you do not desire {3,4,3} but instead desire
- {10,0,0}. In this case you want to maximize A, subject to minimizing
- D and H. (but this is nice and linear)
-
- >I wrote:
- >>There's no way to express the preference, for instance, of those who
- >>might mainly want some kind of coherence and consensus of purpose in
- >>the parliament, for efficiency, and aren't as concerned about getting
- >>their own first choice of representative into it.
- >
-
- However, there is a process to *minimize* the error you make, if you
- want {3,4,3}. The voter can vote randomly, and observe the outcome.
- If the voter wants {3,4,3} and votes for D and the outcome is {2,6,2}
- then the error is {-1, 2, -1} and then the next time the voter can select
- A or H.
-
- In a large enough system (enough voters) which is efficient (ie information
- is relayed back to the voter, elections are frequent enough). The voter
- can vote-observe-correct in order to make knowledgeable, and obvious choices
- to maximize the outcome he desires.
- >
- >I hope it is now clear what I was trying to say.
- >
-
- I think it is clearer now. (it's also more obvious now that I've thought of
- it in more familiar terms).
-
- Arrow seems to be saying that there is no way to arrange a vote so that
- you can know the exact way to vote in a way that maximizes your preference,
- because this would require knowldge of the election process. Since all
- knowldege is contained within the process itself, the voter can't "outdo/
- outperform" the election/market.
-
- It seems that Arrow implies that only a continuous, efficient process can
- help the voter make the most informed decision.
-
- Either that, or I;m reading too much into it...
- >Keith Ramsay
- >ramsay@unixg.ubc.ca
-
-
- --
- __________________________________________________________________________
- John Paul Morrison |
- University of British Columbia, Canada |
- Electrical Engineering | .sig file without a cause
- jmorriso@ee.ubc.ca VE7JPM |
- ________________________________________|_________________________________
-