Forest Simmons

2005-03-11 22:21:55 UTC

Ted,

Thanks for your thoughtful critique. I have been thinking along similar

lines for different reasons, mainly a desire to achieve IDPA.

Unfortunately, reverse TACC is not monotonic with respect to approval. If

the winner moves up to the top approval slot without also becoming the CW,

she will turn into a loser.

However, the following "chain filling" method is monotonic:

Working from top to bottom of the approval list, fill in a chain by

incorporating each candidate that can be included transitively. The

candidate at the top of the resulting maximal chain is the winner.

This technique transforms (mutatis mutandi) each chain climbing method

into a chain filling method.

The chain filling slows the descent enough that even the Approval Winner

can win the method without being the CW.

Suppose for example that pairwise A beats B beats C beats A, and that the

approval order from greatest to least is A>B>C.

The maximal chain is A>B, without C, which cannot fit into this chain

transitively.

There is no CW, yet the approval winner wins, which could never happen in

reverse TACC.

As mentioned above, I wanted to work top down so that I would come to the

Pareto dominators before getting to the Pareto dominated candidates.

Then it doesn't matter if the Pareto dominated candidates are eliminated

at the beginning; the rest of the chain will be the same, including the

top candidate.

[If approval ties are broken by random ballot, then Pareto dominators will

be above Pareto dominated candidates.]

Filling the chain does indeed give us full monotonicity as well:

If the winner moves up relative to any of the other candidates, either in

approval or pairwise, the chain remains the same, since the approval order

of the rest of the candidates is the same, as well as their pairwise

comparisons with each other, and it doesn't matter at what stage the top

member of the chain is added in, as long as it is not later than before.

My Best,

Forest

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Election-methods mailing list - see http://electorama.com/em for list info

Thanks for your thoughtful critique. I have been thinking along similar

lines for different reasons, mainly a desire to achieve IDPA.

Unfortunately, reverse TACC is not monotonic with respect to approval. If

the winner moves up to the top approval slot without also becoming the CW,

she will turn into a loser.

However, the following "chain filling" method is monotonic:

Working from top to bottom of the approval list, fill in a chain by

incorporating each candidate that can be included transitively. The

candidate at the top of the resulting maximal chain is the winner.

This technique transforms (mutatis mutandi) each chain climbing method

into a chain filling method.

The chain filling slows the descent enough that even the Approval Winner

can win the method without being the CW.

Suppose for example that pairwise A beats B beats C beats A, and that the

approval order from greatest to least is A>B>C.

The maximal chain is A>B, without C, which cannot fit into this chain

transitively.

There is no CW, yet the approval winner wins, which could never happen in

reverse TACC.

As mentioned above, I wanted to work top down so that I would come to the

Pareto dominators before getting to the Pareto dominated candidates.

Then it doesn't matter if the Pareto dominated candidates are eliminated

at the beginning; the rest of the chain will be the same, including the

top candidate.

[If approval ties are broken by random ballot, then Pareto dominators will

be above Pareto dominated candidates.]

Filling the chain does indeed give us full monotonicity as well:

If the winner moves up relative to any of the other candidates, either in

approval or pairwise, the chain remains the same, since the approval order

of the rest of the candidates is the same, as well as their pairwise

comparisons with each other, and it doesn't matter at what stage the top

member of the chain is added in, as long as it is not later than before.

My Best,

Forest

----

Election-methods mailing list - see http://electorama.com/em for list info