[EM] "Power" in Approval voting

[Craig Carey]

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.