From: jmorriso@ee.ubc.ca (John Paul Morrison)
Subject: Re: Voting Systems (was Re: Proportional representation)
Organization: University of BC, Electrical Engineering
Date: Tue, 10 Nov 1992 23:23:46 GMT

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 |  
________________________________________|_________________________________
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