[EM] Election-Methods Digest, Vol 62, Issue 10

[James Gilmour]

> Behalf Of Stephen H. Sosnick   > Sent: Saturday, August 29, 2009 2:06 AM
> When summarizing PR-STV, Raph Frank--like everyone else--says, "Each 
> voter gets 1 vote ...."  In fact, however, getting 1 vote is a 
> special case.  And, unfortunately,  mentioning only that special case 
> gives opponents of transferable-vote systems a politically-effective 
> counter-argument.

This statement is wrong, as is much of the rest of the post.

In STV-PR each voter has one vote and one vote only throughout the entire process.	
That one vote is transferable, in accordance with the contingency preferences marked by that voter on the ballot.	
The one vote must be transferable to obtain proportional representation, the objective of STV-PR.

I suspect the incorrect statements arise from a confusion between the voter's one vote and the voter's contingency preferences,
which can be as few or as many as that individual voter wishes, up to the number of candidates.

If the votes are counted according to the rules used for elections to the Dáil Éireann or to the city council of Cambridge MA, each
ballot will carry one whole vote throughout the entire process and the transfer of one ballot at any stage of the count will
transfer one whole vote in accordance with the instructions on that ballot.

However, those 'whole vote' procedures unavoidably introduce an element of chance into the determination of the winners.  That is
considered unacceptable by many, and so the concept of a ballot having a fractional transfer value was introduced (in 1898).

When an elected candidate has a surplus of votes (more votes than the threshold = quota), that surplus must to transferred if
proportional representation is to be obtained.  The only way to avoid any element of chance in making that transfer is to transfer
ALL of the candidate's ballots, but those ballots must transfer ONLY the surplus of votes.  So obviously, each ballot must be
transferred at a reduced value.

It is at this point that the transfer of ballots (the physical process) must be seen as separate from the transfer of votes (the
calculation process).

There are several different ways of calculating the transfer value of the ballots to be transferred, but these methods all have the
same objective: to leave the elected candidate with one full quota of votes and to transfer the surplus of votes in accordance with
the instructions on the transferred ballots.

Although each vote has now been fractionated, each voter still has only one vote.
Each voter contributes only one vote towards the determination of the result.		
That will remain the case throughout the entire count, no matter how many more times any vote may be further fractionated.


It is extremely important to refer to STV as the SINGLE Transferable Vote, because each voter must have only one vote to ensure PR.
This distinguishes STV from all multiple vote systems, like Multi-Member-FPTP or the Cumulative Vote.  It is also important to
emphasise the Single TRANSFERABLE Vote, because PR cannot be obtained (except by chance) if that single vote is not transferable (as
in the Single Non-Transferable Vote).

James Gilmour




> Instead, what people favoring transferable-vote elections should say 
> is that (1) every valid ballot will cast the same number of votes, 
> and (2) the same outcome will emerge regardless of how many votes 
> each valid ballot casts, whether that number is (a) 1 (which 
> simplifies calculation), (b) the number of open seats (which might 
> be, say, 3), or even (c) merely a letter, say, v. 
> 
> The actual numerical value of v (and whether or not it is specified) 
> does not matter because both the number of votes that a candidate 
> needs for election and the number that a candidate receives will 
> adjust in proportion to v--provided, of course, that v is greater 
> than 0.
> 
> For example, if 3 seats are open, 100 people vote, and each ballot 
> casts v votes, then, for election (though perhaps with a tie-break), 
> a candidate needs at least 100v/(3+1) votes, that is, needs at least 
> 25v votes--and will have them if the candidate is first choice on at 
> least 25 of the 100 ballots (or if the candidate is second choice on 
> at least 50 ballots on which a slate-mate is first choice, or is 
> first choice on 20 ballots and second choice on at least 5 ballots on 
> which an unsuccessful candidate was first choice, etc.). 
> 
> (I might add that, if you prefer to refer to the number or proportion 
> of votes needed to guarantee election, then, as Jan Kok points out, 
> the phrase "at least" in the last sentence should be changed to "more 
> than.")
> 
> In Davis, California, as in many other American cities, voters elect 
> either 2 or 3 members of a 5-member city council every 2 years.  In 
> those elections, a voter may vote for as many candidates are there 
> are open seats, and the leading vote-getters win.  In Nov-2006 and 
> again in Nov-2008, residents voted on whether to introduce ranked 
> voting or, more exactly, on whether to become a "charter city," which 
> would allow use of ranked voting and proportional representation. 
> Opponents of the change, including a widely-read columnist in the 
> town newspaper, kept saying that adopting proportional representation 
> would deprive voters of their second and third votes. 
> 
> To refute this assertion, one needed to explain how a set of ranked 
> ballots is converted into a set of winners--and few member of the 
> public would listen long enough.  So we lost--and Davis remains a 
> "general-law" city.
> 
> To improve chances in the future, we should (1) refer to 
> "Transferable Vote" instead of to "Single Transferable Vote," and (2) 
> arrange--and say--that each ranking ballot casts as many votes as the 
> number of open seats (then, in cities like Davis, the value of v 
> would alternate between 2 and 3).
> 
> Currently, some states (including California) require use of 
> Cumulative Voting when shareholders of a business corporation elect 
> directors, and the changes suggested above might also help persuade 
> some legislatures to allow corporations to use a Transferable-Vote 
> system instead.  Cumulative Voting is intended to ensure that, when 
> two or more seats are open, a bloc of voters, if large enough, can 
> fill at least one of the open seats, and Droop's Transferable Vote 
> system also does that--but does it better.
> 
> With Cumulative Voting, each shareholder may cast a number of votes 
> equal to the number shares owned times the number of seats to be 
> filled.  However, a shareholder must predetermine the allocation of 
> his or her total vote among the candidates.  The allocation is 
> irrevocable, even though it is made with incomplete information.
> 
> With a Transferable-Vote system, each shareholder's ballot could 
> still cast a number of votes equal to the number shares owned times 
> the number of seats to be filled, but the shareholder's total vote 
> now would automatically be allocated as the shareholder would wish if 
> he or she knew how other shareholders are voting.  As a result, 
> Cumulative Voting, like plurality winners, is inferior to a 
> Transferable-Vote system, and, by referring to Transferable Voting, 
> instead of to Single Transferable Voting, we can help people to see 
> this.
> 
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