NetNews Usenet Archive 1992 #26/NN_1992_26.iso/spool/can/general/5305

Internet Message Format | 1992-11-08 | 3.3 KB

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From: [e-mail] (Keith Ramsay)
Newsgroups: can.general,can.politics,soc.culture.canada
Subject: Re: Voting Systems (was Re: Proportional representation)
Date: 8 Nov 1992 23:02:37 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
Lines: 54
Message-ID: <[e-mail]>
References: <[e-mail]> <[e-mail]> <[e-mail]>
NNTP-Posting-Host: unixg.ubc.ca

In article <[e-mail]> [e-mail]
(John Paul Morrison) writes:
[Regarding the Arrow impossibility theorem:]
>I would like to see how this following system is affected. I believe
>that the theorem you mention can't apply in this case.
[...]
>This is similar to the way shareholders elect a board (but not really,
>so don't bother picking on this point).
>
>1. A voter can only vote for one person, no prioritizing
>2. The candidate is elected if he gets at least one vote.
>3. The candidate is actually a delegate, so in parliament, he or she
>   represents as many votes as they received.

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.

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.

It also fails another condition of the theorem, in that it is possible
for a person to cause an option A to be selected instead of an option
B, by deciding to try to get C instead of D. Suppose there are a
number of us who'd like to vote for Smith, but for whatever reason
we'd rather she not have too much power. If, however, she already has
sufficient votes, then we'd rather vote for Jones.

Let A, B, C, and D be possible compositions of the legislature, where
A differs from B only by Smith getting some of the votes Jones got in
case B, and likewise for C and D, where A and B are alternatives in
which Smith gets enormous power, and C and D are alternatives in which
Smith gets either a modest amount or none at all. The condition
described by the theorem, requiring that changing preferences between
A and B will not affect whether C or D is chosen, is violated by this
voting system. By trying to ensure Smith gets a modicum of influence,
we could end up giving her more than we had wanted, or conversely.

The conditions about "independence of preferences" are in some sense
the stiffest constraints placed by the theorem, and are often
violated. It is often possible for it to be the case that if you
prefer A to B to C, you are well advised to vote as if you prefer B
most of all, so as to make sure that B rather than C occurs.  This
"sophistical voting" is what the Arrow conditions are formulated to
preclude, and the upshot is that there always is a price paid for
avoiding it.

Keith Ramsay
[e-mail]