[EM] Trees and single-winner methods

Juho juho4880 at yahoo.co.uk
Thu Mar 15 13:07:01 PDT 2007

On Mar 15, 2007, at 17:18 , Abd ul-Rahman Lomax wrote:

> At 01:45 AM 3/15/2007, Juho wrote:
>> I see candidate withdrawal related problems to be quite different
>> from what I see in the proposed three based method. The biggest
>> problem I see in candidate withdrawal is that if the person/group
>> that makes the decision on withdrawal already knows the given votes,
>> then it is possible to decide the winner in a small group, partially
>> bypassing the opinions that the voters expressed in the ballots. This
>> also opens the door to horse trading or even blackmailing. The
>> proposed method at least is based on giving full information to the
>> voters already before the election and letting the voters decide.
> One person's horse trade is another's sensible compromise.

I agree that the horse trading has also some potential to lead to  
good results. It however carries the risk that some of the negotiated  
topics might be related to the very personal needs of the candidate.  
This potential is of course in some form present everywhere where the  
representatives can make major decisions. In this case they however  
play with their personal interests (to become elected) and the  
candidates are expected to trade (no clear ideological driver that  
would force them to vote in some predetermined way).

I also think that the following scenario is not nice. Based on the  
ballots some candidate seems to win the election, and all the  
supporters are already celebrating - until some of the candidates  
announces his withdrawal in order to get some candidate that suits  
him (personally) better elected.

> Suppose that an election is held and there are three candidates.  
> Let's suppose that the rules are approval and/or rull ranked,  
> perhaps Condorcet, but, as alleged by some could happen, everyone  
> bullet votes. And the three candidates have equal support. What  
> would you do with this election? Elect the candidate with the most  
> votes, even though that would mean electing a candidate who was  
> only approved by one-third of the voters? Or if there was an exact  
> tie, choose the winner by lot, which still has the same result -- a  
> minority-approved winner. And it could be a lot worse if there were  
> more than three roughly equal candidates!
> Now, suppose that a candidate can reassign his or her votes to  
> another. If any two of these candidates can agree on who should  
> win, we'd have a winner who, for two-thirds of the voters, it is  
> true that they either chose the winner or the winner was chosen by  
> someone who they preferred as the winner. That seems to me to be  
> *far* better than choosing without such a reassignment.

Note that the votes could have been:
17: A>B>C
17: A>C>B
17: B>A>C
17: B>C>A
16: C>A>B
16: C>B>A

Candidates A and B agree than the winner is A. The "B>C>A" voters may  
be very angry to B.

Note also that the tree based method that I proposed has the option  
that A and B could have agreed BEFORE the election that they form a  
team (a branch in the tree). Maybe they are two Democratic candidates  
and candidate C is Republican. It is probable that either of them  
will win (without negotiations, just based on how the voters voted).  
The "A>C>B" and "B>C>A" voters may need to rethink if they are happy  
with the possibility that their vote to the AB alliance may benefit  
also their least liked candidate. In this case it is however probable  
that the sizes of those factions are less than 17 (since Democrat  
oriented voters are likely to have the second best Democrat candidate  
ranked second).

> And it could get even better if the candidates holding  
> redistributable votes are not limited to candidates who were in the  
> original election. That is, two of the original candidates could  
> possibly agree on a *different* candidate who, had this candidate  
> been in the election, would actually have gained a majority. Or at  
> least the two think that this is a good compromise.

Note that voters that would have voted "A>B>C>D", "A>B>D>C" etc.  
could be very angry if A and B agreed to elect D.

> Now, with Asset Voting, all this could be possible. I expect that  
> there would be *many* candidates and others perhaps holding write- 
> in votes; Asset Voting essentially creates an ad hoc electoral  
> college, without the inequities and other problems of the existing  
> electoral college. With many holders of vote assets, we essentially  
> have a new election process, but it can be fully deliberative. (I  
> generally consider bargaining to be an aspect of deliberation, but  
> some political scientists classify it as a third process, along  
> with aggregation and deliberation.)

In places where direct democracy or electing the representatives  
(directly) is not wanted but more indirect decision making structure  
is needed, then a true electoral college is an option. I think such  
need of indirectness in democracy is not that common. Bargaining will  
happen anyway already between the elected representatives. The  
electoral college level might be an unnecessary additional level.

> Of course, you could do as some jurisdictions do: prohibit  
> truncating ballots, using a ranked ballot, and likewise prohibit  
> equating candidates (for equating in last place is equivalent to  
> truncating, I think). In other words, force them to choose. I find  
> this highly undesirable, actually offensive. It creates the  
> *illusion* of a majority winner. If we are going to create a  
> minority winner, at least we should be honest about it!

Note that there are also methods that do something similar  
automatically. IRV in a way negotiates so that one by one the weakest  
candidates are dropped. But instead of allowing the dropped candidate  
to donate his votes to someone the voter of the voters will be  
redistributed to their second preferences.

Btw, reflecting my earlier comments on the tree structure and the  
fact that it was agreed already before the election, it could be  
better not to allow the dropped candidates to decide after the  
election but they would have given their preferences already before  
the election. In this case voters would maybe bullet vote candidate X  
who would have published his preferences ("A>B>C") already before the  
election. In this case the bullet vote to X would actually be a  
ranked vote "X>A>B>C".

> Now, suppose you don't like the possibility of secret deals. Aside  
> from making private communication illegal -- a cut off their arms  
> to prevent them from being broken solution -- secret deals can't be  
> avoided entirely. After all, a candidate can withdraw *before* the  
> election, based on some "secret deal." But consider an election  
> process that is Asset, *but* whatever result comes must be ratified  
> by the voters, if no majority winner emerged from the intial vote.
> This would be somewhat similar to top-two, but without the  
> inflexibility of top-two (which can pass over a centrist  
> candidate). We have proposed that Range elections might have a  
> ratification stage, or possibly a runoff between the Range winner  
> and a Condorcet winner, if they differ. In this proposal with  
> Asset, a runoff could be between a winner agreed upon by a majority  
> of recast votes under Asset, and, say, a Range or Condorcet winner  
> from the original election. (I have not thought about how Range  
> could be integrated with this, I just mention it because it might  
> be interesting.)

In principle it would be possible to eliminate all candidates that  
have no proof of being potential winners using some agreed criterion,  
and continue with the remaining candidates. But I'm waiting for  
someone to propose rules for such a method.

> I disagree with those who refuse to consider deliberative process  
> as election methods. To me, an "election method" is a like a black  
> box. If we neglect the nomination process -- really we shouldn't  
> --  we have as inputs to the black box markings on a ballot from  
> voters, and the output is a choice between options open to  
> selection. What happens in between defines the election method. And  
> deliberation could be used.

Maybe the most common way to implement a deliberative process is to  
use a some proportional method to elect multiple winners and then let  
those representatives negotiate and decide.

> I've noted before that standard deliberative process actually  
> combines, if the participants want it, Range and Condorcet. The  
> basic process of someone moves that so-and-so be elected, the  
> motion is seconded, and then it is open to debate and amendment --  
> including amendment to name a different candidate -- should,  
> followed by awake participants who can talk with each other --  
> select a Condorcet winner even if all the votes are Yes/No. This is  
> because the participants can literally run every necessary pairwise  
> election. (Most of those elections wouldn't be necessary, so it  
> would be much more efficient than actually running every potential  
> pairwise election.)
> And it would satisfy Range with the provision that a majority  
> could, as we have often suggested, reject the Range winner if they  
> were not satisfied that the compromise involved was beneficial to  
> the society involved.

The proportional representation that I discussed above is quite close  
to Range style utility search.


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