[EM] Wikipedia

Tom Ruen tomruen at itascacg.com
Sat Jun 5 01:34:01 PDT 2004

It looks like I should get involved here since I was told in the Talk section of Wikipedia that I've started a storm by a kind but cryptically named user "Pm67nz"

I have not been subscribed to email for the EM list since May 17 since the election-methods-list at yahoogroups.com reflector was shut down.

Eric Gorr has emailed me directly against the idea of classifying "one vote" methods as plurality and runoff, while leaving Condorcet all by itself in a unique category.

Reading some of the replies here, it would appear what is apparent to me is not apparent to others. The separation of "single vote" methods and "multiple vote methods" would seem a clear one at least to me.

By definition Plurality is "one person, one vote".
Runoffs and IRV are also "one person, one vote" because in any given count every voter can offer at most one vote and in order for a new count to be made, all previous counts have no effect on the new count.

In contrast:
Approval is definitely NOT "one person, one vote" since we're electing one candidate and voters can support as many candidates as they like.
Similarly Borda is definitely NOT "one person, one vote". 
Similarly Bucklin is NOT "one person, one vote" because if a second round is needed, each voter can simultaneously support two candidates.

Of these methods Bucklin is the only one that I've heard was implemented in a political election.

There's a article online that talks about Bucklin being implemented and being rejected on constitutional ground. The article is defending STV and saying previous implementation of ranked ballots using Bucklin was unconstitutional because it allowed more that one vote, in contrast to STV which is a single vote system, and therefore constitutional.
************************** SELECTED TEXT FROM LINK *************
Constitutional Challenge. In Minneapolis, advocates of a 2001 charter amendment to adopt Single Transferable Vote for municipal elections ran into opposition from the city's charter commission. The commission's attorney brought a 1915 Minnesota Supreme Court decision, Brown v. Smallwood 7, to the body's attention. Several commission members cited this case as a basis for the body's recommendation against putting the proposed charter amendment question before the city's voters.
Brown v. Smallwood involved a preferential voting system adopted by the city of Duluth in its 1912 charter and a municipal judgeship created by the Legislature in 1913. 8 The Duluth system asked voters to rank the candidates according to their preferences, but did not use the Single Transferable Vote method to count votes and determine the winner. Instead, a vote-counting procedure known as "the Bucklin method" was used.9 

In the Bucklin vote-counting system, if no candidate received the majority of first choices, all second choices were added to the first choices already tallied, and vote totals were checked to see if any candidate reached the new majority threshold. Thus, in contrast to Single Transferable Vote, under Bucklin some voters' votes were counted more than once, and a second-choice vote for a candidate could work as a vote against one's first choice.

To see how this is true under the Bucklin system, consider a voter who casts a first vote for candidate A, a second choice vote for candidate B, and one "additional choice" vote for candidate C. If candidate A had a plurality, but not a majority, of first choice votes, then the voter's second choice would be added to the number of first choice votes B received, along with the second choices of other voters. Thus, the voter's second choice for B has the effect of undermining his first choice, A by giving B more total votes (first- plus second-choice votes) than A. This is why, while 12,313 voters cast ballots in the 1915 Duluth election, the total number of "votes" counted (including first, second, and additional choices) was 18,860.10 

These flaws of the Bucklin plan -not present in Single Transferable Vote -- led the Minnesota Supreme Court to declare the Bucklin system unconstitutional. The Court first noted that the Minnesota Constitution provided that every male age 21 or older was "entitled to vote" in elections. The Court then said that, when the Minnesota Constitution was framed, 

  the word "vote" meant a choice for a candidate by one constitutionally qualified to exercise a choice. ... It was never meant that the ballot of one elector, cast for one candidate, could be of greater or less effect than the ballot of another elector cast for another candidate. It was to be of the same effect.11

Guided by this definition of "vote," the Court concluded that Duluth's Bucklin voting system had the effect of giving more than one vote to some voters and was thus unconstitutional. The Court was particularly troubled by how the Bucklin system put voters in a position of undermining the prospects of their first choices when they indicated lower preferences:

  The preferential system directly diminishes the right of an elector to give an effective vote for the candidate of his choice. If he votes for him once, his power to help him is exhausted. If he votes for other candidates he may harm his choice, but cannot help him.12

In contrast to the unconstitutional Bucklin system, Single Transferable Vote not only does not share this infirmity, it clearly possesses the qualities the Court said were required of a voting system. In a similar election under Single Transferable Vote, each voter would have one vote which would be counted for each voter's highest preferred candidate who was eligible to receive it. The total number of votes would never change (except for voters who failed to name a second or subsequent choice, whose votes would be considered as being exhausted if their first choice candidate was dropped after the first round of counting). The practical effect would be no different than having a runoff election to narrow the number of candidates to two, except that it would occur instantaneously.13

Thus, a full reading of Brown v. Smallwood shows the Court invalidated the Bucklin system not because it was a preferential voting method per se, but because it had the effect of giving some voters more than one vote, and because it did not permit the voters to fully and effectively support their first choices. Because Single Transferable Vote does not share this fatal flaw, there is no reason to believe that the Supreme Court would hold that Brown v. Smallwood would prohibit a city from adopting Single Transferable Vote for its municipal elections. 

Every method I grouped under "multiple vote" would have the same constitutional judgment. Granted this case specifically only refers to Minnesota, but it would appear to be a universal position as well considering that only "single" vote methods, methods where voters are only allowed to support a single candidate with a single votes are used in political elections worldwide.

Does anyone know a single locale anywhere in the world that has political elections for single winners that uses a "multiple vote" method?

If this is true, if "one vote" methods are exclusively used in politics and "multiple vote" methods exclusively NOT used, why is this distinction so apparently controversial?

Again, granted that Condorcet I take as a special case, not clearly fitting in either category.

Perhaps I am wrong to make this distinction second most important to (number of winners). Perhaps the fact that Condorcet methods defy the division, some other approach is better. I don't know. I judge Condorcet is fundamentally different and deserves its own classification.

If "number of active votes" is unacceptable criterion, then I can see value in "Ballot type" and also "Counting type". There are "single vote", "rank vote", and "rate vote" ballots that are distinct. There are also "one count" methods and "multiple count" methods.

Specifically Plurality, Borda and Approval  are all "one count" methods, a single number applied immediately to each candidate and top number wins. These deserve some separate recognition from their more complex alternatives in each ballot category.

If I were to group by "ballot type" first and "number of vote counts" second:

1. Single vote ballot
    A.. Single count
        * Plurality - count votes, top wins
    B. Multiple counts
        I. Elimination
            * Two round runoff (keep top two)
            * Slow elimination runoff (elimination bottom one)
        II. No elimination
            * Exhaustive Runoff (no forced elimination)
2. Rank preference ballot (1,2,3,...)
    A.. Single count
        * Borda - count votes by ranking value (Value=MAX_RANK-rank)
    B. Multiple counts
        I. Elimination
            * IRV - bottom elimination runoff
            * Supplementary vote  - top two runoff
            * Coomb - disapproval elimination runoff
        II. No elimination
            * Bucklin - approval runoff
            * Condorcet - fixed N*(N-1)/2 pairwise vote counts among N candidates
3. Ratings ballot - assign independent values in range [a,b]
    A.. Single count - count value votes, top votes win.
        * Approval Ratings: No/Yes - point value 0 or 1.
        * Cardinal Ratings - assign independent whole numbers a and b.
        * Generalized Ratings - any finite real number in range [a,b], effectively equivalent to real range [0,1]
    B. Multiple counts
        * MCA - like Approval but with range [0,2] and multiple counting rounds.

That might be more acceptable to members on this list. I added a third level: Multiple counts whether there is forced elimination involved. (You might argue single count methods have forced elimination also, but it is irrelevant since there's no recount after the elimination.)

I'd still defend the issue of "number of active votes", between systems as an important issue worthy to discuss.

Tom Ruen


[EM] Wikipedia 
Eric Gorr eric at ericgorr.net 
Fri Jun 4 21:49:03 2004 

  a.. Previous message: [EM] Wikipedia 
  b.. Next message: [EM] Wikipedia 


At 11:58 PM -0400 6/4/04, James Green-Armytage wrote:
>So far, I don't fully understand why is IRV a "single vote method", Borda
>count a "multiple vote method", and Condorcet a "pairwise vote method",
>when they are all ranked ballot single-winner systems that can be
>conducted in a single round. There's probably some justification for it,
>but at first look I find it to be more confusing than helpful.

I am not aware of any justification. These changes seem to have been 
made summarily.

>I think that the single-winner vs. multiple winner distinction is a good
>one to make first.
>Then I'd probably go to the ballot type.

Are there really more then just three ballot types?

As near as I can tell, every election method has a ballot that would 
look like one of these:

Approval - the voter selects one or more candidates

Ratings - the voter assigns a score to one or more candidates

Ranked - the voter only expresses a preference between candidates

I have no idea what might be placed in a miscellaneous category.

What ballot would not be covered by one of these three?

In Plurality, for example, the voter is only allowed to select a 
single candidate, putting it in the Approval category.

Approval is not, in my opinion, appropriately assigned to the Ratings 
category since the voter does not assign a score to a candidate.

== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20040605/4c4bc7e0/attachment.htm>

More information about the Election-Methods mailing list