[EM] Condorcet vs Approval

[Ultra Runner]

Forest Simmons wrote:
>
> I have ambiguous feelings about my two favorite methods.
> 
> Sometimes it seems like Condorcet is over-elaborate, making fine
> distinctions between the deck chairs on the sinking Titanic. (How's that
> for a mixed metaphor?)
> 
> On the other hand, there are times when Approval strategy leaves me in a
> quandary about whether or not I should extend my approval down into the
> 40% utility level to help keep a zero utility candidate out of office.
> 
> I have a couple of suggested compromises starting with Condorcet and
> moving towards Approval, but stopping short of ordinary Approval.
> 
> I.  Condorcet.  I prefer the version of Condorcet that allows voters to
> give a partial preference list, with all unlisted candidates considered to
> fall below the last listed candidate. (These implicit preferences are
> counted along with the explicitly marked preferences.)  If voters were
> instructed to list (only) their APPROVED candidates in order of preference
> (and leave their unapproved candidates off of the preference list), this
> would be one small step in the direction of approval.
> 
> To put teeth into the instruction, voters should be informed that if there
> is a Condorcet cycle of winners, then that tie will be resolved by the
> approval scores ... all of the listed candidates will be considered
> approved, and the non-listed candidates unapproved. 
> 
> Alternatively, before this drastic cycle breaker is applied, the
> preferences among the approved could be discounted by half to see if that
> less drastic action would resolve the cycle.
> 
> II. In this second method the voters are instructed to indicate which
> candidates are approved and which candidates are highly approved, and to
> cross off the other candidates from the ballot, for good measure. 
> 
> The ballots will be scored by the Condorcet method (head-to-head counts)
> with H>A, H>U, and A>U, where H, A, and U stand for any members of Highly
> approved, Approved, and Unapproved, respectively.
> 
> If this method results in a Condorcet cycle among the top candidates, that
> cycle can be broken by gradually discounting the H>A preferences as in
> Method I above. 
> 
> Well, there they are.
> 
> Note that both of these methods retain the same level of immunity from
> insincere voting that Condorcet and Approval enjoy.  In particular, in
> method II, if I prefer C to D, and I confer High Approval status on D,
> then there is no reason to with-hold that status from C. 
> 
> In method II how would I decide where to draw the lines between the
> three categories?
> 
> I would draw the line between Approved and Unapproved on the same basis
> that I do now.  After having done that I would choose between the Highly
> Approved and the (merely) Approved using exactly the same strategy with
> the Unapproved totally removed from consideration.  (Pretend they don't
> even exist.) For this inside strategy calculation the probabilities and
> expectations would be conditioned on the event that the winner is to be from
> among the approved. 
> 
> One simple way to mark the ballots for method II would be to cross off
> all the Unapproved names (with one or more lines through the name so that
> it can no longer be read by the machine) and to mark the Highly approved
> names by filling in the machine readable dot.  Any name that was not
> crossed out or marked by the usual dot would be considered (merely)
> Approved.
> 
> If nothing else, these two methods help elucidate the close relationship
> between Condorcet and Approval.
> 
> Bye for now,
> 
> Forest
> 
> 
> 

Ultra:

Great!  Method II would be easy to apply to Craig's example (utilities of 100, 25, 20, and 0, repectively, for candidates A, B, C, D, having respective poll approvals of 36, 40, 45, and 44.)

I would "approve" ABC, and "highly approve" only A.


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