Jobst Heitzig heitzig-j at web.de
Thu Mar 1 05:39:48 PST 2007

Dear Forest,

you proposed UncAAO:
> UncAAO stands for Uncovered, Approval, Approval Opposition.  Here's
> how it works:
> For each candidate X,
> if X is uncovered,
> then let f(X)=X,
> else let f(X) be the candidate against which X has the least approval
> opposition, among those candidates that cover X.
> Start with the approval winner A and apply the function f repeatedly
> until the output equals the input.  This "fixed point" of f is the
> method winner.
> ["Approval opposition" of X against Y is the number of ballots on
> which X but not Y is approved.]

It would be interesting to compare this to other monotonic and 
clone-free methods that always pick the winner from the uncovered 

For example "total approval chain climbing" (TACC), a method I proposed 
a long time ago: Construct a chain of options by starting with an empty 
chain, then processing the options in order of ascending approval 
score, and adding the option at hand to the chain iff that option 
pairwise beats all options already in the chain; the winner is the 
option added last to the chain.

Like UncAAO, also TACC has many good properties but also a main 
disadvantage: Because we start with the least approved option, the 
result depends too much on "noise" options. 

It seems UncAAO is much more robust against adding noise candidates, but 
can we prove that it fulfils related conditions like IPDA or ISDA etc.? 
Is the result even independent from options outside the Smith set? 

Yours, Jobst

> This method requires a tally of both pairwise approval and pairwise
> ordinal information, but both are efficiently summable in N by N
> matrices, where N is the number of candidates.
> This method (UncAAO) is monotone, clone free, and always picks from
> the uncovered set, which is a subset of Smith.
> Zero info strategy is sincere.
> Even perfect info incentives for burial and betrayal are practically
> nil.
> As near as I can tell, the only bad thing about the method is the
> "tyranny of the majority" problem shared by most, if not all,
> deterministic methods.
> Comments?
> Forest
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