[EM] Buying Votes

[Jobst Heitzig]

Dear Greg,

you wrote:
> I wish I knew how FAWRB worked...

I will give a new step-by-step exposition of FAWRB in a new thread 
during this day.

> Most people say the majority criterion is a good one. I, for one,
> doubt its importance. I was merely saying that a counter-criterion
> inconsistent with the majority criterion hasn't really been offered.

That counter-criterion has been offered: "Every voter should have full 
control over the same amount of winning probability." Methods complying 
with this then should try to increase the efficiency by providing some 
means for anonymous cooperation.

> umm... in any electoral method some subset will have absolute power...

What makes you think so? The simplest counter-example to your claim is 
Random Ballot.

> Also, in ANY electoral method you can get useless votes.

Again: The simplest counter-example to this claim is Random Ballot.

> For example, if I have 999 people supporting me under some
> non-majoritarian method, 1 person voting against it won't make a hell
> of a lot of difference. The 999 have complete power!

The question is not whether it makes "a hell of a lot of difference" but 
whether it makes a difference at all. In FAWRB, you would have incentive 
to provide that 1 person with some small amount of compensation in order 
to get her vote, too.

> This is a gripe with democracy not with majoritarianism.

Nope. See above. It's all about *establishing* democracy!

> Thinking outside the box, they could secede.

Yes, and that's a threat to society which could ultimately lead to anarchy.

> Athenian democracy doesn't work. Sorry. Using a non-determinstic
> method incurs massive flaws in real life.

Give examples, please. Athenian democracy worked well for the Athenians 
for two centuries.

> Applying the same logic to majoritarian methods, every opinion has a
> given probability of being a majority.

That probability being zero when the opinion is the minority opinion.

> Yay we agree OMOV is trivial. Why do you keep bringing up violations
> of OMOV then? 

I did never talk about OMOV, it was you who brought it up. Probably you 
misunderstood me.

> Denying voters influence is an OMOV flaw. 

No it's not. Most majoritarian methods comply with OMOV and still deny 
the minority any influence. I'm asking myself how often I will have to 
repeat this obvious fact.

> If there are a group of int(.5*voters)+1 people who vote X > non-X and
> X is one and only one candidate, how does the minority express its
> opinion w/o violating OMOV.

Er? You ask how they express their opinion? Well, on the ballot, of course?

> They ARE better, just not intrinsically so. Specific violation of a
> given property does not a perfect voting system make.

Nobody is claiming that since it would be ridiculous.

> Is there ever an incentive not to secret contract? If so, is it significant?

To avoid this is exactly the task of the method designer. The method 
should be designed so that there are positive incentives to cooperate 
when the compromise is good enough.

> I see... is this FAWRB?
> 
> Candidates have three statuses on a ballot: Favorite, Approved, Disapproved
> 
> I pick two ballots at random.
> 
> If there is a candidate that is favorite on both ballots, pick it.
> 
> If there is a candidate that is favorite on the first and approved on
> the second, pick it.
> 
> If there is a candidate that is approved on the first and favorite on
> the second, pick it.
> 
> If there is a candidate that is approved on both the first and second, pick it.
> 
> Otherwise pick the favorite on the first.

That's more or less what we call D2MAC, which is similar in spirit to 
FAWRB and achieves the task of electing a good compromise, too. The main 
difference is that with D2MAC compromise options which are only good but 
not *very* good have fewer chances than with FAWRB.

> Ok now the actual criticism. I know that FAWRB is nondeterministic.
> Here is why that is bad.
> 
> Factions (both unwilling to compromise):
> 
> A 55%
> B 45%
> 
> you view A as gaining a "55% chance of victory".
> 
> This reasoning is flawed. Instead of viewing A as getting .55 victory
> units, think of it as a random choice between two possible worlds:
> 
> A-world and B-world
> 
> A-world is 10% more likely to occur, however they share remarkable similarities.
> 
> In both worlds >=45% of the people had no say whatsoever.

They had a "say" in that they had a fair chance. In reality, chance 
occurs everywhere anyway. Picking an option is always a risky thing. 
When economists talk of utility and analyse preferences they almost 
always mean *expected* utility because the actual utility is the result 
of a random process.

Anyway, the point is that in your example people (if they use the right 
decision method) will have an incentive to find a compromise C which 
everyone likes a lot better that the 55%/45% lottery. So they will 
usually reduce the randomness by cooperation.

> Now, you're reasoning apppears to stem from a simple observation...
> "If A achieves one more vote, its chance of victory increases, hence
> everyone has a say!"
> 
> That reasoning, while correct, leads to a flawed conclusion.
> 
> The average number of wasted votes or the people who, for a particular
> election, had no impact on the election is HIGHER.

Increasing the winning probability *is* having an impact.

> The only difference is that adding one more vote causes the
> probability to increase. It isn't that any of the results are more
> fair (A-world and B-world are still equally as good and bad,
> respectively), it's just that the illusion of choice exists.

It's no illusion. In the long run, the 55% will get their will in about 
55% of all decisions, and the 45% will get their will in about 45% of 
all decisions. Under a majoritarian method, the 55% will get their will 
in 100% of all decisions and the 45% will get their will in 0% of the 
decisions.

> Let me explain please. Any non-consensus method enables a particular
> group to victimized at the whim of a larger faction. FAWRB allows
> this, it is simply probabilistic so the victims feel like they have a
> shot.

There will usually be no victims because people will cooperate to elect 
a compromise which everybody likes better than the Random Ballot lottery.

>> To me it makes no essential difference whether the dictator is one person or
>> a group of persons. So, in principle, majoritarianism qualifies as
>> dictatorship, too.
> 
> By that logic, anything that makes a decision is a dictatorship.

Again, no. The difference is whether I can be sure to get my will 
*before* having to decide how I behave in the decision process. 
Dictators and majorities in a majoritarian system can know they can have 
their will, so they have no incentive to compromise. In a 
non-deterministic method, the faction whose option turns out to be the 
winner in the end *does not* know before that this will occur, so their 
voting behaviour will be based on expected utilities, and this *does* 
give them incentives to compromise.

Yours, Jobst