[EM] Re: Election-methods digest, Vol 1 #167 - 9 msgs

[Clinton Mead]

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>Message: 1
>Date: Tue, 15 Jul 2003 13:05:20 -0700 (PDT)
>From: "Alex Small" <asmall at physics.ucsb.edu>
>To: <election-methods at electorama.com>
>Subject: [EM] Question for STV-PR supporters
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>I have an honest question for people who think that STV-PR and related
>methods are the best way to implement proportional representation in
>public elections.  I'm not trying to be combative, I'm just curious.
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>How many members should a typical legislative district elect?  I doubt
>anybody would seriously propose using STV to elect representatives for,
>say, a 50-member district, since the number of candidates might be a few
>hundred.  Obviously voters wouldn't have to rank all 300 candidates or
>whatever, but the ballot would still be pretty imposing.
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>So what district size would you recommend?  Or, what is the typical
>district size in places that use STV-PR for public elections?
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>Note:  I'm not in the same camp as Approval supporters who say "Voters
>don't want to/aren't well-informed enough to rank all of the candidates"
>when the number is, say, 10.  But I personally would have a hard time
>ranking 100 candidates, and I'm pretty sure most other people would too.
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>Alex
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In my state of NSW, Australia, there are 40 positions for the upper 
house of my states government. Members hold their seat for 2 terms, so 
20 seats are available each election. We had well over 200 candidates 
running. Unfortuantly, this makes the ballot paper look like a table 
cloth, but the voting system is in the constitution. There are also 
boxes for each group, which people can just number a 1 in that box. That 
turns the vote into a vote for that parties candidates in order of 
preference along party lines. Most people (>99%) just number one box 
above the line, instead of numbering the minimum of 15 boxes below the 
line.

Personally, I think it would be better just to eliminate below the line 
voting (voting for individual candidates), and let candidates form their 
own groups at their choice. Each independent could form its own group. 
Groups could have a brief listing of names. This would reduce the size 
of the ballot paper from over 200 boxes to about 20. The actually 
process of counting would be the same (STV).

A bit about proportional representation. For me, proportional 
representation systems should follow these criteria, in decending order 
of importance.

- total votes / (positions available + 1) < quota <= (total votes + 1) / 
(positions available + 1)

1. Proportional Representation: If there is a set of candidates X, and 
there are Y votes that rank candidates in X above all candidates not in 
X, at least int(Y/quota) candidates from X shall be elected or all 
candidates in X shall be elected.

2. Clone Proof: If there is a candidate A in an election, who is not 
elected, there shall be a way of adding a new candidate B to all votes 
such that B's position relative to all non-A and non-B votes is the same 
as A's to all non-A and non-B votes, and this shall not cause A or B to win.
(This could be stronger)

3. Monotonicity: If there are two candidates A and B, and on vote V, A 
is ranked higher than B, and there is no candidate C such that A is 
ranked higher than C and C is ranked higher than B, then swapping A and 
B on vote V shall not cause A to be elected if it was previously not 
elected, and it shall not cause B not to be elected if it was previously 
elected.

STV seems to pass criteria 1 and 2 for proportional representation, 
which is fairly good. It is also the system we use in Australia to 
select the Australian senate, after the embrasing situation in the 50's 
where 33 out of the 36 members of the senate belonged to the same party.

Is there a system that passes all three of the above criteria? I've been 
thinking about this, and I can't seem to get monotonicity and 
proportional representation to go together. Or is this the start of a 
new arrows theorem, there is no "proportional representation system" 
(even when we don't include Independence From Irrelevent Alternatives).

Clinton Mead.