[Election-Methods] [english 92%] Re: a strategy-free range voting variant?

[Jobst Heitzig]

Dear Peter,

You wrote:
> Let's imagine the following votes from the deciding voters:
> 
> 10 million:   Nader: 10   Gore:  5   Bush:  0
> 41 million:   Gore:  10   Nader: 5   Bush:  0
> 49 million:   Bush:  10   Gore:  5   Nader: 0
> 
> Let's say that the lottery winner was Bush. 

That doesn't matter since not the actual outcome of the lottery but the 
lottery itself is the benchmark. By this I mean that the rating of the 
lottery is to be computed as the expected rating of the lottery winner 
given the lottery probabilities.

Never the less, this doesn't change much for your criticism:

 > The real winner
> is going to be Gore, with 705 million voting money units,
> while Bush has only 490 million. The total rating difference
> is 215 million. Do you want to modify each deciding voter's
> account with that big amount?

I must admit that I apparently only though about small electorated like 
some dozens of people. Now I see that we have to do something about this.

One way could be to use not equal sized groups of benchmark, deciding, 
and compensating voters, but use only a small number of deciding voters. 
But that would diminish the method's efficiency considerably.

Another idea is to change the transfer formula so that the transfers get 
smaller in landslide elections. The reason why I have the hope that this 
should be possible without destroying the strategy-freeness is that 
there is already some other transfer formula that works: the Clarke tax 
- just as you said.

The Clarke tax means: Transfer the amount I specified only for those 
deciding voters who are "swing" voters, that is, for each voter for 
which the removal of her ballot would change the winner. If we use this 
scheme instead of mine, then a deciding voter's account is always 
adjusted by some negative value between zero and her rating difference 
between the actual winner and the alternative winner which would result 
without her ballot. This is a well-known scheme which is discussed in 
the paper I cited.

However, as Warren's webpage nicely points out, the Clarke tax also has 
a problem with large electorates: It will almost never have to be paid 
since the probability that there are swing voters is very small.

So, I'm pretty sure that there must be a middle way between the far too 
seldom transfers of the Clarke tax and the far too large transfers I 
suggested, especially since these both schemes don't differ in the 
amount of the transfer but only differ in the condition when it is 
applied...

Any suggestions are welcome!

Yours,
Jobst

> 
> You can try to diminish this modification by the fixed fee but
> I guess the modification will still be very high, because you are
> not able to precisely predict the votes not to mention who the
> lottery winner is going to be.
> 
> And I guess if you try to eliminate this huge voting money
> transfer by some averaging operation, you will bite your
> other finger by ruining the strategy-freeness.
> 
> Even if these worries are valid, this random partitioning of the
> electorate looks a witty idea, worth some other trials.
> 
> I also like the idea of voting money, but with some reservations;
> if the value of the voting money is not bound exactly to some
> real value, then good-bye, strategy-freeness, I guess.
> 
> Otherways, voting money can be used even with the classical
> Clarke-tax. Yes, Clarke-tax goes to one direction, but every
> voter on every day can get one voting money unit.
> 
> If my voting money does not grows (except by votings), I will
> use the most amount of it when I'm afraid to die soon - why
> keep them if I can't use them?. So there seems to be some
> extra voting power on the part of the deadly ill.
> 
> Peter Barath
> 
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