From: rossw@sco.COM (Ross Wetmore)
Newsgroups: can.general,can.politics,soc.culture.canada
Subject: Re: Proportional representation
Date: 11 Nov 92 14:18:03 GMT
Organization: SCO Canada, Inc.

In article <1992Nov6.123920.21484@access.usask.ca> (Gerry Gryschuk) writes:
>From article <1d9q47INN68t@iskut.ucs.ubc.ca>, by mathew@unixg.ubc.ca (Mathew B Englander):
>> dat@thinkage.on.ca (David Adrien Tanguay) writes:
>>>What are the cons of a transferable vote system? (i.e., where the voter ranks
>>>all candidates, somewhat similar to the way the party leaders are chosen)
>>>It would seem to preserve the ideological direction of the electorate, yet
>>>limit the representation to the more popular parties, helping to avoid
>>>parliamentary deadlock.
>> 
>> The greatest problem is that candidates can be hurt by an *increase* in
>> support. For example, suppose that candidates A, B, and C are running 
>> for the party leadership. Suppose that there are 675 voting delegates
>> divide roughly into four groups:
>> 
>> 	Group I: 150 voters, whose ordered preference is A, B, C
>> 	Group II: 100 voters,  "      "        "      "  A, C, B
>> 	Group III: 200 voters, "      "        "      "  B, C, A
>> 	Group IV: 225 voters,  "      "        "      "  C, A, B.
>> 
>> (What I mean here is that, for example, Group II prefers A to C, but
>> prefers C to B -- and thus presumably prefers A to B.)
>> 
>> Now, what happens in the vote? On the first ballot, the results are
>> 
>> 	A: 250 (Groups I and II)
>> 	B: 200 (Group III)
>> 	C: 225 (Group IV).
>> 
>> No candidate has a majority, and since B has the lowest total he is
>> eliminated and A and C have a "runoff". Note now that the 200 voters
>> in Group III will now vote for their 2nd-favourite candidate, C.
>> So the second ballot results are
>> 
>> 	A: 250 (Groups I and II)
>> 	C: 425 (Groups III and IV).
>> 
>> And C wins the leadership.
>> 
>> So far, so good. But what would have happened if, before the first
>> ballot, C did some last-minute campaigning and won over all the members
>> of Group II (which gets renamed Group II*). The breakdown of groups now
>> becomes:
>> 
>> 	Group I: 150 voters, whose ordered preference is A, B, C
>> 	Group II*: 100 voters, "      "        "      "  C, A, B
>> 	Group III: 200 voters, "      "        "      "  B, C, A
>> 	Group IV: 225 voters,  "      "        "      "  C, A, B.
>> 	
>> Since C has increased her support, and she would have won even without
>> this increase, we would expect her still to win now. But does she?
>> The new first ballot results are:
>> 
>> 	A: 150 (Group I)
>> 	B: 200 (Group III)
>> 	C: 325 (Groups II* and IV).
>> 
>> So A is eliminated, and Group I supports its second choice, B, on the
>> second ballot:
>> 
>> 	B: 350 (Groups I and III)
>> 	C: 325 (Groups II* and IV).
>> 
>> So B wins! The shift of voters *toward* C actually caused C to lose
>> the race. This is why this sort of voting is fundamentally flawed.
>> 
>
>Sorry I don't normally leave in the whole post just to respond a little at
>the end but I think it's necessary here.
>
>Anyway, yes this method would be flawed. However a simple fix would be to
>set a fixed number of "points" to the place a person voted a candidate.
>Simply base it on the number of candidates running and no problem should
>arise. That is in your examples a first place vote is worth 3, second 2 and
>3rd 1. In this case C wins both times and by a wider margin in the second
>scenario as she should. The math is left as an excercise for the reader.
>--
>Gerald Gryschuk            Saskatoon,Saskatchewan = a place with 9 months

  I should have gone back to the original post by Matthew, but it has 
flushed :-)

  Since in the example, as has been pointed out, any pairwise runoff
would yield a different result, there is no strong preference in the
electorate and choosing any single candidate should perhaps best be 
done by a lottery technique in such pathological cases :-).

  However, both of you seem to think that 'C' gaining support but losing
is a flaw in the STV system. I think this results from looking at a
projection of the results along one dimension of a multi-dimensional
voting system, if I can make the mathematical analogy.

  Think of it this way. STV does not just count simple voting majorities,
but weights the general sentiment of the electorate by the subsequent
preferences. In increasing 'C' support by reducing 'A', 'C' also reduces
the opposition to 'B'. Since 'B' is the real threat to 'C', and not 'A'
working hard on this set of voters is a mixed blessing, and with the
given set of figures, obviously a negative effect. By ignoring the real
strength of the antipathy to C by B voters, and the different dynamics
of STV which tries to minimize such strains in the outcome by choosing
not the leading candidate, but the one with the most broad based appeal,
you can clearly come up with a case for a flawed argument. But I think
the logic needed to argue this is unfortunately based on the flaw of
trying to judge the quality of apples by how orange their colour is. STV
uses a multi-dimensional weighting, not just first round or single vote
support.

  It is like the converse flaw in strict PR. I get just one vote, and
while my preferences may be for either of two of the top 5 parties,
there is no way for me to express that sentiment. Thus single issue
parties with little broad based appeal can find their proportional
weight in the final result much higher than the general support for
their party would warrant. This is actually critical, since the selected
representatives are going to be voting on a large number of issues, and
not just one or two special interest policies.

  But I agree to some extent with Gerald, that a modification of STV that
weights the second and later round strength slightly less (but not
necessarily as strongly as say getting one point for every candidate
you beat) is perhaps a reasonable way to better estimate the broad based
support or opposition. That is people obviously 'feel' stronger about a
candidate if they vote for him/her in early rounds.

  Of course, the NULL candidate should also be on the ballot, ie one need
only make a positive vote for candidates one supported. 
---- 
Ross W. Wetmore - (416)922-1937 x259    | RFC822net: rossw@scocan.sco.COM
SCO Canada Inc, Toronto, Ont, Canada.   | UUCP:{uunet,utcsri}!scocan!rossw
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