[EM] Remember Toby

[Jameson Quinn]

2011/6/8 Juho Laatu <juho4880 at yahoo.co.uk>

> Here are some random observations about the SODA method.
>
> There should be a full definition of the method somewhere.
>

I've posted a full definition. However, this definition included my
additional step of recounting the top two without mutually-delegated votes.
In further off-list conversation with Forest, I've realized that this
addition, while it may be marginally helpful, does not fundamentally change
the dynamics of the situation, and so is not worth the extra complexity.
Here's the full definition without it:

1. Before the election, candidates (including declared write-ins) submit
full rankings of other candidates. Equality and truncation (equal-bottom) is
allowed in these rankings. These rankings are made public.

2. Voters submit approval ballots, with up to two write-ins. "Do not
delegate" is a valid write-in.

3. All approvals are counted for each candidate. Bullet votes for each
candidate are also counted. These totals are made public.

4. After a brief period (probably a couple of weeks) for analyzing and
discussing these first-round results, all candidates, in a simultaneous and
temporarily-secret ballot, decide how many rank levels (from their initial
ranking in step 1) to delegate to. They may not delegate to candidates they
ranked at the bottom (since this is strategically identical to delegating to
nobody and withdrawing from the race). If A delegates to B, a number equal
to A's bullet votes is added to B's approval total.

5. The candidate with the highest approval total after step 4 wins.


>
> If there are three candidates and their declared preferences are A>B>C,
> B>C>A and C>A>B, the method may introduce some additional problems. If most
> voters delegate, then we may easily have a cycle (easier than usual). It
> will not be easy to decide who will delegate votes to the others.
>

Actually, the strategy in such a cycle is simple and stable. Say C has the
fewest bullet votes. C has no hope of winning, so C delegates to A, so B
delegates to C, so A delegates to B. B wins - the minimax winner. No further
changes (either adding or subtracting delegations) will be strategically
advantageous, so this is a strong equilibrium.

Things are not necessarily quite so simple if there are more than 3
candidates. But in order for things to be strategically ambiguous (where
some random "mixed strategy" is favored), I think (though I have no proof)
that you need at least 5 candidates in the Smith set - which I regard as a
negligible possibility, certainly under 1% in real-world conditions.

>
> If we have a centrist candidate (C) and left wing (L) and right wing (R)
> candidates, then it is problematic for C to decide whether to declare C>L>R
> or C>R>L. Some of C's right wing oriented supporters might be lost if C
> decides to declare C>L>R.
>

Well, they could just vote [C,R]. If things are as you say, this should be a
relatively safe option, because C is almost guaranteed to be a CW.
(Formally: if there are negligible numbers of [R,L] voters, either directly
or delegated, then a [C, R] vote is strategically the same as a C>R>L vote.)


> C could ask for help from a less known person C2 to take part in the
> election C2's declared preferences could be C2>C>R>L. Now the right wing
> oriented supporters of C will have a more sensible way to vote. Since C will
> not not rank C2, there is not much risk that C2 will be elected.
>

This would work too.


> One step further, maybe C could be allowed to give two preference orders,
> C>L>R and C>R>L. Then we are not far from allowing any preference order and
> full rankings.
>
> The votes could be delegated in multiple ways. The nominated candidate
> could decide how many to approve (in one or several phases).
>

One phase.


> The nominated candidate could delegate the vote to the next one in chain so
> that the next one in chain would get also the right to delegate (or not) the
> vote further (using the original preference order).
>

No.


>
> There is some smoke in the room in the sense that always when some
> nominated persons are given the right to decide the destiny of large number
> of votes (=delegated power), there is a possibility of trading the votes.
> One can imagine that some candidates would take part in the election only or
> mainly for this purpose - to get some votes and then decide how (how far in
> the chain) to sell them.
>

Say X's declared preference order is A>B. They can only be decisive if,
without their vote, B leads by less than the votes they hold. Generally
speaking, that's a 50/50 proposition that their trick is useless.

And even then, their choices are:
-Support A, electing A (which is so "obvious" that it would hardly deserve a
payback, except insofar as X had legitimately demonstrated that they had a
constituency of supporters);
-Support neither, electing B (certainly not a way to get a payback)
-Or support A and B, electing B.

The latter case is the only likely one where anything untoward has happened
- X has not strategically followed their declared preferences. I think that
mercenary X's like that would be generally reviled, to the point where it
would be in B's propaganda interests to pre-declare that they weren't
willing to play ball with such extorsions.

Also, remember that an X supporter can easily vote [X, A] if B is
sufficiently unpalatable. If there are enough such voters, it would be in
X's interest to truncate B from their ranking, which would make a smoky-room
deal all the more unlikely.

Essentially, the point is that if A didn't win this election, the room would
have been slightly smoky, but the voters would know exactly whom to blame:
X. X could not claim to have been acting from deep ideological reasons,
unless the payback was some actual policy commitment beneficial to their
supporters; and if that were the case, well, that's democracy at work.

On balance, I'd claim that the extra transparency from the pre-election
rankings is a bigger step than the small possibility of smoky-room results.



----

I'll continue to argue that SODA is great, and that the fact that it's the
most pareto-dominant over plurality is important. But it seems clear that
there are a number of people on this list who prefer Condorcet methods in
general, and I doubt that further argument is going to change that. So,
here's a proposal. The condorcet-supporters choose one simple method to
propose (it seems that Minimax-WV and Condorcet/Implicit Approval are the
strongest contenders right now, if you don't count systems which are
designed to occasionally give spoiled elections), and we put that method and
SODA forward as proposals (while still endorsing a wide range of methods) in
the (opt-in) statement that we craft.

Remember, in order to sign such a statement, you would not have to agree
that the two proposals were the best two systems (probably nobody believes
this), just that they were both practical proposals and both improvements
over plurality. I would happily do so; I hope others would join me; and I
don't think we'll find any short list which would get a similar level of
buy-in.

Sound good?

Jameson Quinn
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