Approval Vote: reply to Bart Ingles

[Bart Ingles]

Craig Carey wrote:

> >Bart Ingles:
> >> The only constraint with approval voting is that a voter is allowed one
> >> vote per candidate.
> 
> You of course mean the Approval Vote sub-votes, but the vote itself being
>  a real number (or if integers are insisted upon, then rationals).

Most people refer to approval votes simply as "votes", not sub-votes. 
To distinguish this from the collection of approvals/non-approvals given
by an individual voter to the various candidates in a race, I refer to
the collection as a ballot.


> >I should have said "The only constraint with approval voting is that a
> >voter is allowed to give either 0 or 1 vote to a given candidate."
> 
> The value 1 is selected if the voter provides a preference ranking, (an
>  integer between 1 and k, k = the number of sub-votes).

Not sure what you mean here.  You can reasonably take first choice in a
ranking to imply approval, and last choice to mean non-approval, but you
can't infer either solely from the middle choices in a ranking.


> >It would be possible to have a system where the voter is allowed to give
> >a fractional vote between 0 and 1 to a candidate, but it would never
> >make sense to vote that way -- optimal strategy is always to give either
> >0 or 1 votes.  Thus the system would be equivalent to approval voting,
> >except that the additional possibilities might confuse ignorant voters.
> >
> 
> Until some numbers on giving the weights are given, that paragraph hasn't
>  a lot of clarity or weight. The words "optimal strategy", i.e. strategy
>  of the method designer, is perhaps a implicit reference to Ossipoff's
>  "utility" idea.

The words "optimal strategy" refer to strategy from the viewpoint of a
voter who is trying to maximize his own utility (i.e. trying to get the
best 'deal' for himself or maximize his own impact on the election
outcome).

In other words, if you have a point system where the voter is allowed to
assign up to 10 points to each candidate, a voter's best strategy would
be to give each candidate either the maximum 10 points, or none at all. 
Thus such a system is equivalent to approval voting.


> ////////////////////////////////////////////////////////////////////////

> ---------------------------------------------------------------------------
> Consider the Borda said to be of D. G. Saari:  Case 3 candidates:
> 
>   A..  Za0    2t . (2, 0, 0)

                      ^ I think this should be (1, 0, 0)


> ---------------------------------------------------------------------------
> Consider the 4 formula of the given 'Standard Borda' passes P2. I find that
>  it doesn't for 4 candidates. It does pass P2 for 3 or less candidates.
> 
> P2({0}): Passes if winners unaltered on adding (t,t,t,t) to
>  (Za0,Zb0,Zc0,Zd0):
>                      A    B    C    D
>   A...  Za0    t . ( 3,  1/3, 1/3, 1/3)

                     ^ should be (3, 1, 1, 1)

In other words, equally ranked candidates get the points they would have
received if fully ranked, but allocated equally.  B,C,and D would have
received a total of 3 points (2 + 1 + 0), so each gets 3/3 = 1 point
(under standard Borda).

Saari's version would simply collapse unranked choices into one
position, so the above ranking would receive (1,0,0,0) under his
method.  The ranking A(BC)D would receive (2, 1, 1, 0); under standard
Borda it would be (3, 1.5, 1.5, 0).

> ---------------------------------------------------------------------------
> 
> Voters are not constrained by "reason". If any wants to define a constraint
>  of reason, then let's have that in an existential logic form.

Nobody claimed that the voters are so constrained, but it makes sense to
have a system whereby a voter can maximize his result by voting
rationally.
 

> Anyway, when trying to find out if the method fails the rule, it is most
>  certainly reasonable to examine the method in the very regions where it
>  fails that rule.
> 
> When there are 4 candidates, then specifying the last preference can alter
>  the set of winners.


Using that argument, what system doesn't fail?  With approval voting,
voting for all candidates is a form of abstention.  If you abstain under
STV, can't that alter the set of winners?


> >> >This example is not really sufficient to predict voter strategy, since
> >>
> >> You wrote about "efficiency" in text deleted, and questioned my using
> >>  3 votes for one voter, which indicates a viewpoint difference.
> >
> >I mentioned "Condorcet efficiency" and "social utility efficiency", but
> >I haven't a clue what those have to do with using 3 votes per voter.
> >
> >
> >> Suppose a person was ignorant and didn't use enough Approval sub-votes.
> >
> >He would presumably still have voted for his more highly-favored
> >candidates.  He may not have supported the necessary compromises, but
> >you can do the same with any other system.
> 
> Suppose he/she just voted for one candidate; the method will cause a vote of
>  that type to lack power. If Approval Vote is implemented in a real election
>  then there 'should be' a TV or pamphlet publicity effort funded by the
>  government that educates voters on what a bad method it is, and how they
>  should not cast too few sub-votes, e.g. out of mistaken presumption that
>  the method is fair and democratic and does not give an undue unfluence to
>  those individuals that will vote randomnly for half of the, say 88,
>  candidates. Suppose one of the 88 was the current president fighting of
>  scores of no hopers fattened in industry, and the same president that twice
>  led the nation to military victories in the previous 4 years against foreign
>  dictators.

Maybe they should hire you to write the pamphlet.  :-D)))