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Another proposal.

There was one point that I tryed to make in my initial post about unusual behaviour of supermajorities and quorums, that Andrew Pimlott summed up more nicely than I did.

Andrew Pimlott wrote:
> Any method in which an option can be eliminated "early"--ie, without
> a fully head-to-head with all the other options--has the same
> fundamental flaw as instant runoff, and should be rejected for the
> same reason.

> So for example, the clause, in most drafts, that first eliminated
> options that were defeated by the default option, was a direct
> invitation to insincere strategic voting. It would encourage voters
> to put the default option second, in an attempt to knock out the
> other candidates early. Exactly what we're trying to avoid with the
> Condorcet method.

With that clear explaination, and my somewhat vague examples in my post, the "default option" thats drops defeats early seems to encourage strategy, and should not be used.


When I made my previous proposal, I incorrectly assumed that all non-default options would have identical supermajority and quorum requirements, which Raul Miller almost immediately pointed out as incorrect, and shortly following Anthony Towns illustrated a practical example of having non-default options without supermajority requirements.

With this proposal, I've tryed to achieve two main goals, which have seem to eluded previous drafts at least as far as I can tell, and in particular my own attempts.

(i) Supporters of options that require supermajorities can not use the strategy of introducing a weak non-supermajority candidate to the benefit of their supermajority restricted candidate. (Reduce Strategy)

(ii) Re-running an election with the new winner and default with identical votes produces identical results. (Consistency)

Both of these properties seem to be closely related to the implimentation of the default option, so I've toned down its effects, in particular this implimentation does no early defeats.

In the process of trying to achieve the above two goals, its likely I've broken other things, but its worth a try.

In any case, I have a vague feeling that maybe this might actually work a little.


- Definition: Defeat is the normal defeat, not considering supermajority and quorum requirements.

- Definition: A super-defeat is a defeat after considering supermajority and quorum requirements.

(a) The default option is considered.

(i) If option A has quorum requirements and supermajority requirements less than or equal to option B, and option A defeats option B, then option A is considered.

(ii) If option A super-defeats all options with quorum requirements or supermajority requirements less than option A, then option A is considered.

Perform CSSD on all considered options, ignoring supermajority and quorum requirements.

(Keep a close eye on the or's and and's in the rules in part (b))


To illustrate the properties of this method, I'll use an example.

For simplicities sake, assume we have two sets of options, one requiring supermajorities (the non-default group), and the other which doesn't (the default group).

The default option is a member of the default group.

Rule (i) immediately makes sure all members of the smith set of the default group are considered, at least.

For members of the non-default group, these members can not use rule (i) to be considered, as members of the non-default group do not have quorum and supermajority restrictions less than or equal to the only currently considered options in the default group.

So they must use rule (ii) to be considered. This means they have to super-defeat, that is, over their supermajorities, all options which have super-majority or quorum requirements less than themselves. That is, for a option in the non-default group to be considered, it must beat all options in the default group. This removes the strategy of adding weak options to the default group, as all options in the default group have to be defeated anyway. [Reduce strategy]

However, after one option of the non-default group is considered, other members of the non-default group can begin to be considered also, just by defeating that considered non-default group option using rule (i). This prevents identical elections from producing different results, and if a supermajority is achieved, it is awarded to the most prefered option first time, instead of after a re-election with identical votes. [Consistency]

Also, the ignoring of supermajorities and quorums in the final resolution of considered options (c) further improves consistency due to identical propositions between options in elections with identical votes.


Anyway, hope you all enjoy finding an example to break this proposal into little pieces, and then maybe even salvage it and improve it.


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