From: jmorriso@ee.ubc.ca (John Paul Morrison)
Subject: Re: Voting Systems (was Re: Proportional representation)
Organization: University of BC, Electrical Engineering
Date: Sun, 8 Nov 1992 07:47:32 GMT

In article <1dhqfrINNrjv@iskut.ucs.ubc.ca> mathew@unixg.ubc.ca (Mathew B Englander) writes:
>leei@lightning.mcrcim.mcgill.edu (Lee Iverson) writes:
>>This discussion is interesting but sadly uninformed.
>>
>>There is a well-known theorem which essentially says that there is no
>>system of voting system which accurately reflects a system of
>>preferences without introducing paradoxes (i.e. situations in which
>>moving up in the rankings of some subset of voters will actually cause
>>someone to do worse)!

I would like to see how this following system is affected. I believe
that the theorem you mention can't apply in this case.
>
>
[ theorems ]

>1. There should not be a dictatorship (i.e., the choice cannot simply be
>	that of one individual; other voters must be able, somehow,
>	to influence it)
>2. A candidate should not be hurt by an increase in support
>3. A shift from one candidate to a second should not hurt a third candidate
>	in favour of a fourth candidate
>4. There should be at least three candidates, and voters should not
>	be restricted in their choices among ranking these candidates
>5. A system that would choose one candidate over a second, and that second
>	candidate over a third, should also choose the first candidate
>	over the third.
>
>Arrow's theorem showed that under any voting system, one of these axioms
>is violated.

I do think you need to qualify "any voting system", but anyway, please
demonstrate where this system does indeed lead to a paradox.

(btw,  4. might be crucial to his proof, but I don't see why we have to 
abide by it. At least one candidate, is all that must be required)

This is similar to the way shareholders elect a board (but not really,
so don't bother picking on this point).


1. A voter can only vote for one person, no prioritizing
2. The candidate is elected if he gets at least one vote.
3. The candidate is actually a delegate, so in parliament, he or she
   represents as many votes as they received.
4. The delegate can only apply his votes in one way in any parliament
   vote (he can't split them into different factions). I don't think
   this should need spelling out, but I did anyway.
5. It probably doesn't matter how ridings are divided, since each vote
   the delegate/candidate carries represents one person. But for
   sake of argument, let's say ridings are divided into equal population
   sizes, and a candidate can only run in one riding.


- This system cannnot elect a dictator (rather the opposite I'd say)
- More votes just means more clout for the delegate, so more votes do
  not hurt him.
- Shift of support cannot hurt support for another
- Assumption 5 doesn't apply, because all candidates are effectively chosen
  but the delegates vary in how far their vote will go in parliament

So you really have to qualify (ie restrict your voting system) in order
to make paradoxes show up. A delegate system doesn't fit into the same
mold.

Now, for making things more efficient, you would have to raise the number
of votes a delegate  must get, before being allowed to represent people.
This might confirm the paradox. 

TO ensure that it's impossible to elect a dictator,
because only 1 delegate ran, you could make enough ridings, so at least one
would run in each riding. THings like salary would have to be proportional
to the number of votes. I think the size of parliament would be
self limiting, because people wouldn't run unless they could win enough votes
to justify the work involved. By-elections would be impossible though, 
unbless you kept track of votes, or made everyone re-run again.
This kind of system might lend itself well to an electronic system of voting,
where the overhead in debating and voting in one place would be lower.
This is as close to "true" democracy as you could ever get, without having
everbody get involved and pay attention and vote all the time.

(why is this similar to shareholders electing a board? because a block of
shares can ensure that there is a seat on the board, and the block usu.
gets enough seats on the board to keep within proportion. It is different
because usu. one person own all the shares, which would not be the
case here)

Interestingly, this system is like the financial industry, where you "vote"
with your investments, and put your money where you think it will be best
represented. 
>
>
>Mathew Englander.


-- 
__________________________________________________________________________
 John Paul Morrison                     |  
 University of British Columbia, Canada |  
 Electrical Engineering                 |   .sig file without a cause
 jmorriso@ee.ubc.ca              VE7JPM |  
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