[EM] Election-Methods Digest, Vol 62, Issue 10
Stephen H. Sosnick
shsosnick at ucdavis.edu
Fri Aug 28 18:05:42 PDT 2009
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.
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.
At 12:01 PM -0700 8/28/09, election-methods-request at lists.electorama.com wrote:
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>Today's Topics:
>
> 1. Explaining PR-STV (Raph Frank)
> 2. Re: Explaining PR-STV (Jan Kok)
> 3. Re: Explaining PR-STV (Raph Frank)
>
>
>----------------------------------------------------------------------
>
>Message: 1
>Date: Fri, 28 Aug 2009 14:08:28 +0100
>From: Raph Frank <raphfrk at gmail.com>
>To: Election Methods <election-methods at lists.electorama.com>
>Subject: [EM] Explaining PR-STV
>Message-ID:
> <e01ff3490908280608h528b86f7ja39a03a521888c75 at mail.gmail.com>
>Content-Type: text/plain; charset=ISO-8859-1
>
>One of the hardest parts about PR-STV is actually explaining it.
>
>Anyway, this was an approach I was thinking of.
>
>I think it hits the main points by covering the reasons rather than
>the detailed maths. Most people in PR-STV countries understand the
>method, as they experience it from a voter's perspective, rather than
>a counter's perspective.
>
>
>PR-STV is based on 4 main principles
>
>1) Each voter gets 1 vote and they can vote for any candidate they want.
>
>** All votes are equal. **
>
>2) The 5 candidates who get the most votes get a seat.
>
>I am assuming 5 seats are to be filled, but the system works for any number.
>
>3) If you vote for a losing candidate, your vote is transferred to
>your next choice
>
>This reason for this rule is is so that you can safely give your first
>choice to your favourite even if he is a weak candidate.
>
>If he doesn't win, your vote will be transferred to your next highest
>choice, until it gets to a candidate who can win a seat.
>
>** Voting for a weak candidate doesn't mean you are "throwing your
>vote away". **
>
>4) If you vote for a candidate who gets more votes than he needs, the
>surplus is transferred to your next choice.
>
>The Quota is simply the minimum number of votes a candidate needs in
>order to be guaranteed to be one of the top 5.
>
>If 5 candidates had a quota of votes, then even if all the rest of the
>votes go to one of the other candidate, he would have less than the
>quota.
>
>If you vote for a candidate and he gets twice the Quota, then he only
>needs half of your vote to get elected.
>
>He keeps half of your vote and the rest of your vote would go to your
>next choice.
>
>** Voting for a strong candidate also doesn't mean you are "throwing
>your vote away". **
>
>The Ballot
>
>The ballot allows the voter the rank the candidates (who is your
>favourite candidate, who is your next favourite and so on).
>
>** This gives the voter full control over how their vote is transferred. **
>
>The Count
>
>In the first round, all the first choices are counted.
>
>If no candidate is greater than the quota, then the weakest candidate
>is eliminated and his votes are transferred.
>
>Otherwise, the candidate with more than the quota is declared elected
>and his surplus votes are transferred.
>
>This is repeated round by round until all 5 seats are filled.
>
>--
>
>There would need to be a discussion on the loss (or lack thereof) of
>the "local-link" due to the larger constituencies and unstable
>governments. Also, there would need to be a discussion of
>proportionality. For example, show some first past the post results
>and some PR-STV country results.
>
>Also, there could be a discussion of the effective threshold due to a
>small number of seats.
>
>If there was an example of the count, it might also be worth giving
>the viewer an example ballot that is his ballot. You could then say
>stuff like "unfortunately, your first choice (A) didn't get elected,
>so your vote goes to your next choice (B)".
>
>
>------------------------------
>
>Message: 2
>Date: Fri, 28 Aug 2009 08:30:46 -0600
>From: Jan Kok <jan.kok.5y at gmail.com>
>To: Raph Frank <raphfrk at gmail.com>
>Cc: Election Methods <election-methods at lists.electorama.com>
>Subject: Re: [EM] Explaining PR-STV
>Message-ID:
> <fe3681d30908280730q134a3efbv3f0e0d46c260c724 at mail.gmail.com>
>Content-Type: text/plain; charset=ISO-8859-1
>
>This is a very nice, clear explanation or PR-STV. I would suggest
>mentioning that the quota is commonly set at greater than 1/(N+1)
>times number of valid votes. Thus, with 5 seats and 600 votes, a
>candidate who gets more than 100 votes is guaranteed a seat.
>
>I'm not convinced that PR can lead to "instability." Isn't that more a
>property of the parliamentary system? After all, in the US we can have
>congress be at 50/50 Dems/Republicans, where just one defection can
>swing control to the other side, yet our government doesn't seem all
>that "unstable".
>
>Cheers,
>- Jan
>
>On Fri, Aug 28, 2009 at 7:08 AM, Raph Frank<raphfrk at gmail.com> wrote:
>> One of the hardest parts about PR-STV is actually explaining it.
>>
>> Anyway, this was an approach I was thinking of.
>>
>> I think it hits the main points by covering the reasons rather than
>> the detailed maths. ?Most people in PR-STV countries understand the
>> method, as they experience it from a voter's perspective, rather than
>> a counter's perspective.
>>
>>
>> PR-STV is based on 4 main principles
>>
>> 1) Each voter gets 1 vote and they can vote for any candidate they want.
>>
>> ** All votes are equal. **
>>
>> 2) The 5 candidates who get the most votes get a seat.
>>
>> I am assuming 5 seats are to be filled, but the system works for any number.
>>
>> 3) If you vote for a losing candidate, your vote is transferred to
>> your next choice
>>
>> This reason for this rule is is so that you can safely give your first
>> choice to your favourite even if he is a weak candidate.
>>
>> If he doesn't win, your vote will be transferred to your next highest
>> choice, until it gets to a candidate who can win a seat.
>>
>> ** Voting for a weak candidate doesn't mean you are "throwing your
>> vote away". **
>>
>> 4) If you vote for a candidate who gets more votes than he needs, the
>> surplus is transferred to your next choice.
>>
>> The Quota is simply the minimum number of votes a candidate needs in
>> order to be guaranteed to be one of the top 5.
>>
>> If 5 candidates had a quota of votes, then even if all the rest of the
>> votes go to one of the other candidate, he would have less than the
>> quota.
>>
>> If you vote for a candidate and he gets twice the Quota, then he only
>> needs half of your vote to get elected.
>>
>> He keeps half of your vote and the rest of your vote would go to your
>> next choice.
>>
>> ** Voting for a strong candidate also doesn't mean you are "throwing
>> your vote away". **
>>
>> The Ballot
>>
>> The ballot allows the voter the rank the candidates (who is your
>> favourite candidate, who is your next favourite and so on).
>>
>> ** This gives the voter full control over how their vote is transferred. **
>>
>> The Count
>>
>> In the first round, all the first choices are counted.
> >
>> If no candidate is greater than the quota, then the weakest candidate
>> is eliminated and his votes are transferred.
>>
>> Otherwise, the candidate with more than the quota is declared elected
>> and his surplus votes are transferred.
>>
>> This is repeated round by round until all 5 seats are filled.
>>
>> --
>>
>> There would need to be a discussion on the loss (or lack thereof) of
>> the "local-link" due to the larger constituencies and unstable
>> governments. ?Also, there would need to be a discussion of
>> proportionality. ?For example, show some first past the post results
>> and some PR-STV country results.
>>
>> Also, there could be a discussion of the effective threshold due to a
>> small number of seats.
>>
>> If there was an example of the count, it might also be worth giving
>> the viewer an example ballot that is his ballot. ?You could then say
>> stuff like "unfortunately, your first choice (A) didn't get elected,
>> so your vote goes to your next choice (B)".
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
> >
>
>
>------------------------------
>
>Message: 3
>Date: Fri, 28 Aug 2009 15:45:58 +0100
>From: Raph Frank <raphfrk at gmail.com>
>To: Jan Kok <jan.kok.5y at gmail.com>
>Cc: Election Methods <election-methods at lists.electorama.com>
>Subject: Re: [EM] Explaining PR-STV
>Message-ID:
> <e01ff3490908280745g4ac2e12bqf2cd7e1a75963ec9 at mail.gmail.com>
>Content-Type: text/plain; charset=ISO-8859-1
>
>On Fri, Aug 28, 2009 at 3:30 PM, Jan Kok<jan.kok.5y at gmail.com> wrote:
>> This is a very nice, clear explanation or PR-STV.
>
>Thanks. My aim was to get down to the reasons for each of the rules.
>
>PR-STV is an attempt to solve the issues with PR-SNTV.
>
>> I would suggest
>> mentioning that the quota is commonly set at greater than 1/(N+1)
>> times number of valid votes. Thus, with 5 seats and 600 votes, a
>> candidate who gets more than 100 votes is guaranteed a seat.
>
>I was aiming for zero maths formulas.
>
>I am not sure how much it really adds. The important point is that
>the quota is the number of votes you need to be sure of being
>guaranteed to be 5th or better. The exact way of calculating it is
>not important.
>
>Anyone interested in the maths would be able to work it out pretty
>quickly from
>
>"If 5 candidates had a quota of votes, then even if all the rest of
>the votes go to one of the other candidate, he would have less than
>the quota."
>
>Also, the way I define it, the Droop quota is the only one which meets
>the condition.
>
>> I'm not convinced that PR can lead to "instability." Isn't that more a
>> property of the parliamentary system? After all, in the US we can have
>> congress be at 50/50 Dems/Republicans, where just one defection can
>> swing control to the other side, yet our government doesn't seem all
>> that "unstable".
>
>Plurality will take a 55 to 45 split in support and magnify that into
>say a 65 to 35 split in seats.
>
>However, PR with lots of parties is less likely to swing to extremes.
>If a centerist party holds balance of power, then if they shift
>support the resulting government will still probably be generally
>centerist (just leaning in the other direction).
>
>I think also the point is that if a small party ends up with balance
>of power, that creates an incentive for new parties (and independents)
>to arise.
>
>
>------------------------------
>
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>End of Election-Methods Digest, Vol 62, Issue 10
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