[EM] "Power" in Approval voting

[Owen Trimmer]

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Regards
Owen Trimmer

> -----Original Message-----
> From:	Craig Carey [SMTP:research at ijs.co.nz]
> Sent:	Saturday, 11 March 2000 02:29
> To:	election-methods-list at eskimo.com
> Subject:	Re: [EM] "Power" in Approval voting
> 
> 
> On power of voters. A method that gives a voter too much power
>   is not a fair method. The Economist said Saari's Borda method
>   is fair and it is not. I previously wrote that some Borda
>   methods were fair and the contradiction, i.e. error, is that
>   my previous statement were false. I note that The Economist
>   magazine printed a false and misleading statement about the
>   Borda method in saying or if saying, it was fair. I don't
>   suppose it matters if the error came from Donald Saari.
> 
> There might be a dispute here on whether a voter's power should
>   be defined in such an arbitrary narrow contrived way that the
>   Approval Vote is allowed to pass.
> 
> I gave 2 definitions that allow the power of a voter. Such
>   definitions won't be the last word because they do not apply
>   to STV and all preferential voting methods with papers like
>   what STV accepts. That was my "P4 sketched" method, or 5Mar00.
>   It said an upper limit in voter's influence/power would exist,
>   but there would not be a lower limit.
> 
> 
> At 16:21 08.03.00, MIKE OSSIPOFF wrote:
>  >
>  >EM list--
>  >
>  >Craig Carey's objection to Approval, based on a misconception of
>  >power, is probably something that will often be heard when
>  >Approval is proposed. So I'd like to answer it here.
>  >
> 
> To use that word "misconception" suggests that you have the term
>   defined. I need a general definition of the power of a voting
>   paper.
> 
> I may write to Mr Donald Saari and inquire into why Borda is not
>   fair. I presume there is no intent to make it fair. I presume
>   readers of this list and Mr Saari's student are satisfied that
>   Borda is an unfair method, because it is not a method that is
>   used?.
> 
> 
> 
> 
>  >Argument #1:
>  >
>  >As Bart asked, can Craig or anyone else supply an example in
>  >which some voter doesn't have the power to cancel-out any
>  >other voter that he wants to?
> 
> That question is interesting and narrowly constructed. Polticians
>   could have a lot of trouble assuming a viewpoint that allows the
>   Approval Voting method to pass. They can be rapid thinkers,
>   when consider excessive improper hostile influence from unknown
>   'plebs'. And why not AV method advocates too?.
> 
> My power idea is not finally defined, although I gave 2 fomulae.
> One was this: (Min u)(Sum j)abs(weight(j) - u). But that ignores
>   the actual preferences on the papers, and it is far from allowing
>   different types of papers to be grouped and be allowed a common
>   influence/power.
> 
> 
>  >
>  >When Bart asked that question, did Craig post an example? :-)
>  >
>  >To save the trouble of looking for an example--any voter has
>  >the power to cancel-out any other voter in Approval.
>  >
>  >That by itself should settle the issue. But I'd like to comment
> 
> The Approval Voting method is able to be an extremely unfair
>   method. I don't know if it is actually used.
> 
> 
> ----------------
> At 14:17 06.03.00, Craig Carey wrote:
> ...
> 
> :At 00:26 06.03.00 , Bart Ingles wrote:
> :...
> :>If you have candidates A, B, C, and D, and your minister casts a single
> :>'sub-vote' for B (using your terminology), you might represent it as:
> :>(0, 1, 0, 0).
> :>
> :>Any other voter can neutralize it with the following single vote,
> :>consisting of three sub-votes:
> :>(1, 0, 1, 1)
> :>
> :>Since only the exact complimentary vote can precisely cancel out the
> :>minister's vote, the second voter has no leeway to try to cancel other
> :>votes as well.
> 
> ::A lot of voters may want to elect their candidate, not figure out
> :: how to adapt to having 3-200 times more power than they reasoned that
> :: they deserved, knowing that actually using that power could cause one
> :: of their preferred candidates to lose. An option would be to use IRV
> ...
> 
> Two hundred times the proper power is an really realistic figure if
>   the mathematical findings are to remain true for most of the 21st
>   century in each instance where the Approval Voting method is applied.
>   For example, it could be used to elect new leaders to guide a
>   coalition of fragmented factions in a US SciFi community that happened
>   to be supported by some of the sharpest tactical voters around.
> 
> :
> :However, if there are many competing factions and many winners are to be
> : elected, then voters would get extra power to pair them and help cause
> : one of the pair to lose:
> 
> That paragraph is the statement of my argument.
> It is an obvious matter and Mr Ossipoff doesn't understand it then
>   I may not reply (the rest of the readers should be able to figure
>   this out).
> 
> ----------------
> 
> Before ending, I note that old FBC definition did not constrain the
>   number of winners. Mr Ossipoff said he regarded the number of winners
>   to be 1. If that is true then it should be in the definition.
> 
> Does Mr Saari consider Borda to be a multi-winner method?.
>   
> 
> I will stop here, and I might respond to the rest but after I read it.