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

Fri, 28 Aug 2009 18:14:22 -0700

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, [email protected] 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 <[email protected]>
To: Election Methods <[email protected]>
Subject: [EM] Explaining PR-STV
Message-ID:
        <[email protected]>
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 <[email protected]>
To: Raph Frank <[email protected]>
Cc: Election Methods <[email protected]>
Subject: Re: [EM] Explaining PR-STV
Message-ID:
        <[email protected]>
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<[email protected]> 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 <[email protected]>
To: Jan Kok <[email protected]>
Cc: Election Methods <[email protected]>
Subject: Re: [EM] Explaining PR-STV
Message-ID:
        <[email protected]>
Content-Type: text/plain; charset=ISO-8859-1

On Fri, Aug 28, 2009 at 3:30 PM, Jan Kok<[email protected]> 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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