[EM] Has this idea been considered?

[Juho Laatu]

On 6.7.2011, at 6.42, Russ Paielli wrote:

> On Tue, Jul 5, 2011 at 2:14 AM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:
> On 5.7.2011, at 11.19, Russ Paielli wrote:
> 
>> If one wants to simplify the inheritance rules even more then we might end up using a tree method (I seem to mention it in every mail I send:). In that approach there is no risk of having loops in the candidate transfer order. Votes would be counted right away for each branch, and the candidate of the largest brach of the largest branch of the ... would win.
>> 
>> That sounds interesting, but I'm not sure I understand what you mean. Can you give an example?
> 
> Here's one example.
> 
> Tree of candidates + number of personal votes + sum of votes of candidates of each branch:
> 
> Branch1 (13)
>     Branch1.1 (7)
>         A (4)
>         B (3)
>     Branch1.2 (6)
>         C (6)
> Branch2 (18)
>     Branch2.1 (12)
>         D (5)
>         E (7)
>     Branch2.2 (5)
>         F (3)
>         G (2)
>     Branch2.3 (1)
>         H (1)
> 
> - Branch2 has more votes than Branch1 => Branch2 wins
> - Branch2.1 has more votes than Branch2.2 and Branch2.3 => Branch2.1 wins
> - candidate E has more votes than candidate D => candidate E wins
> 
> The tree approach thus forces the order of transfer to be non-cyclic. The transfer order of candidate E is E > D > {F, G, H}.
> 
> The tree format can be printed on paper and it is easy to grasp. The ballot sheet may also follow the same tree format. Branches may have names (e.g. party names) or be unnamed. Left wing parties could join forces under one branch. Candidates of one party could be divided in smaller groups. Or maybe the branches have no party names and party affiliations, maybe just descriptive names, maybe no branch names at all.
> 
> 
> Thanks for the example, but I don't understand. Who decides what the branches are, and based on what? Why is E transferring votes if E has the most votes? And what are the counts after each transfer? Sorry if those are dumb questions. 

Maybe the method is simpler than you expected. It could be as well described as a list based method where the "parties" can be internally split in smaller groupings (or they can join also together in larger groups). My references to vote transfers are just to explain how this method relates to methods that use transfers in the vote counting process. The votes that E "transfers" are actually not taken away from him but counted both for him and all the branches that contain him (sorry about using such confusing terms). In this method one can in a way "transfer" all the votes right away to the groups that some candidate is part of. We thus just count the votes of each party / grouping (i.e. sum up the votes to the candidates of that party). Votes are not "transferred" (or summed up) to other candidates but to the branches of the tree (= parties, groups) that represent all the candidates within them. The formal vote counting rules will probably not use term "transfer" at all (maybe "sum" instead).

The numbers in the example show the final counts, where the votes (that were all given to the candidates) have been summed up. The vote counting rule starts simply "the biggest party gets the only seat". In this example Branch2 (= party2 or wing2) is bigger than Branch1, and therefore the only available seat goes to that party. (Note that the tree method could be used as well in multi-member elections.) Then that single seat will be allocated within Branch1 to the biggest of the "party internal" branches, i.e. Branch2.1, and then to E that has more votes than D.

The branches will be decided by the parties or whatever associations or groupings the candidates and their supporters will form. Let's say that Branch1.1 and Branch 1.2 are two left wing parties that nominated their candidates ( {A, B} and {C} ) themselves and then decided to joins forces and form a joint branch (Branch1) to beat the right wing candidates (that was not enough though since the right wing parties did the same thing and got more votes). Or in a two-party country like the U.S. this example would of course be Branch1=Democrats, Branch2=Republicans, and then the candidates of these parties would form some groups within that party. Branch2.1. could contain two similar minded candidates from California. They joined together since they understood that if they would both run alone, they would probably be spoilers to each others and they could not win. Party internal groupings could thus be arranged by the party itself or by the individual candidates that form the sub-branch. It would depend on the election rules who is will formally nominate such groups (party vs. already nominated candidates vs. whatever group of candidates).

From strategic point of view it makes sense to form sub-brances (all the way to a binary tree). Within Branch2 sub-branches Branch2.2 and Branch2.3 could have also joined forces together (and add one extra level of hierarchy in the tree) in order to try to take the victory away from Branch2.1 (they would not have been successful though since together they had only 6 votes).

Parties could also avoid making too many branches in the fear that they would make the party appear or actually "split inside" into different camps. Maybe parties could nominate less candidates because of that. But on the other hand some other party might nominate more candidates and get also more votes this way (since they could nominate candidates that represent a wide variety of voter opinions).

The tree method sets some clear limitations to the inheritance order. But on the other hand these limitations help the poor voters in making their decisions since they need not wonder why candidate A transfers to C although a very similar (in their minds) candidate B transfers to D. In the tree model candidates that think the same way would be forced to join forces and have similar transfer order from some branch point onwards.

Trees make it thus very clear what the individual candidates stand for. And that clear understanding will influence their behaviour also after the election. "Green" and "southern" candidates must decide if they form a green branch that will be internally split into southern and northern sub-branches, or if they form a southern branch that will be further divided in green and some other groups. The more important topics should be used first, closer to the root of the tree. That should make also the inheritance order and relative closeness of different candidates in the tree quite natural (but not perfect since e.g. the green candidates can not first transfer to all the greenish candidates of all the parties and then to their own party).

And of course the voters can not transfer their votes in whatever order. The tree format actually reflects more what the candidates think of themselves than what the voters think about them. This property (that is shared by all methods that are based on transfer order as given by the candidates, like your method) is a good thing in the sense that when candidates clearly say what they stand for, they can not tell different stories to different voter groups in the hope that they would get higher in the preference order of those voters, and voters with false understanding on what some candidate stands for are corrected.

(As a multi-member method trees will also provide very accurate proportional representation between the branches.)

Juho



> 
> --Russ P.
> 
> -- 
> http://RussP.us
> ----
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