<div> Forest W Simmons <fsimmons@pcc.edu> wrote<br>
<br>
> Designated Strategy Voting (DSV) methods relieve the voter of repeated<br>
> returns to the polls for each iteration of the feedback loop, and also<br>
> solve the anonimity requirement, but as has been noted, methods that<br>
> are supposed to iterate unto an equilibrium may not converge.<br>
><br>
> But linear order convergence can be speeded up by making use of a<br>
> convergence accelerator.<br>
><br>
> If a, b, and c are successive numbers in a sequence of iterates where<br>
> the convergence is linear (as per the usual case) then the quantity<br>
><br>
> Q=(a*c - b^2)/(a+c-2*b)<br>
<br>
It depends on how the system works.<br>
<br>
My understanding of DSV is that each vote is considered in sequence.<br>
The voting algorithm has access to the vote totals for all the<br>
candidates to date. This doesn't lend itself to the above process.<br>
<br>
Actually, there is also a method for batch processing. I would<br>
prefer that as it treats all votes equally. <br>
<br>
DSV seems to use plurality as its 'base' voting method.<br>
<br>
Maybe the system should allow strategies to share information about<br>
their internal content, if they wish.<br>
<br>
I would suggest the process for each round would be that<br>
<br>
- each strategy is reset (no memory of previous rounds)<br>
- each strategy is given access to the result of the last round (State)<br>
- each strategy does not know which strategy other strategies are using<br>
- each strategy indicates which communication protocols it supports<br>
- each strategy can open a communication channel with any other strategy<br>
- voting occurs using a number of sub-rounds (perhaps 20)<br>
- no communication is allowed for the sub-rounds<br>
- the sub rounds are<br>
-- each strategy votes<br>
-- results so far are made known<br>
- the end result is the total of all the votes for all the voting sub-rounds<br>
<br>
This gives a clear (though complex) mapping of any state to another<br>
state. The communications would also have to be in rounds so that<br>
they don't change based on voter ordering. Also, a random number<br>
generator would not be made available to the strategies as that<br>
would also make the system undefined ... though that may <br>
eliminate some of the benefits of DSV.<br>
<br>
The communication channels are essential. Otherwise, the base election<br>
method would have a major effect on the result.<br>
<br>
If it is plurality, then centre squeeze will still happen. If there<br>
are 2 candidates with 45% and 47% each, then strategies for the middle<br>
candidate are going to switch. If they can communicate, maybe they can<br>
get the 45% group to side with them as a condorcet/lesser of 2 evils.<br>
<br>
The iteration in this system is multi-dimensional. The<br>
values in each dimension are the total number of votes given to<br>
each candidate.<br>
<br>
e.g.<br>
<br>
X(n) = [a(n), b(n), c(n), ...]<br>
<br>
a(n) = candidate a's vote total after round n<br>
<br>
The simple iterator:<br>
<br>
X(n+1) = f(X(n))<br>
<br>
This can be improved by finding X such that the below is true.<br>
<br>
X - f(X) = 0<br>
<br>
The iterator is:<br>
<br>
X(n+1) = X(n) - f(X(n))/f'(X(n))<br>
<br>
It would apply to each dimension individually.<br>
<br>
I am not sure what the convergence rules are for that formula though.<br>
<br>
Also, since it is multi-dimensional and possibly discontinuous, there may<br>
not be a solution.
<br>
<br>
> In other words, if you were to run the sequence backwards, so that you<br>
> are iterating the inverse of f instead of f itself, then the sequence<br>
> would converge, since if the graph of f has a slope with abs value<br>
> greater than one, the graph of the iinverse of f will have a slope with<br>
> abs value less than one. [Their slopes are reciprocals at the<br>
> equilibrium point.]<br>
<br>
I am not sure an unstable equilibrum point is actually a good thing for a<br>
voting method. It seems to me that it would be making the result worse<br>
on each step instead of better from the perspective of the voters.<br>
<br>
The strategy in the forward direction is designed to improve the current<br>
situation, if you reverse it, then each voter's declared strategy is<br>
trying to make the situation worse for the voters.<br>
<br>
I would probably include a rule that once the point has been found, it<br>
is tested to confirm convergence. (When in the X(n+1) = f(X(n)) 'mode').<br>
</div>
<div> <br>
</div>
<div style="clear: both;">Raphfrk<br>
--------------------<br>
Interesting site<br>
"what if anyone could modify the laws"<br>
<br>
www.wikocracy.com</div>
<div> <br>
</div>
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