[EM] an extra step for IRV (and some other methods?)
I have an idea for adding an extra step to IRV which has the effect of throwing out its compliance with Later-no-Harm in exchange for Minimal Defense, while trying to hang on to Later-no-Help. *Voters strictly rank from the top however many or few candidates they wish. Until one candidate remains, provisionally eliminate the candidate that is highest ranked (among candidates not provisionally eliminated) on the fewest ballots. The single candidate left not provisionally eliminated is the provisional winner P. [So far this is IRV, used to find a "provisional" winner. Now comes the extra step.] Interpreting candidates ranked above P as approved and also P as approved if ranked, elect the most approved candidate.* This method might be called "IRV-pegged Approval" (IRVpA). It is more Condorcet-consistent than IRV, because when IRVpA produces a different winner that candidate must pairwise beat the IRV winner (so it keeps IRV's compliance with Mutual Dominant Third). Also the IRVpA winner must be more approved than the IRV winner. I'd be interested if anyone can show that this fails Later-no-Help. Some other methods might gain from adding the same extra step, for example Schulze(Margins), MinMax(Margins) and Descending Solid Coalitions. It will fix any failures of Minimal Defense (and my Strong Minimal Defense criterion) and Plurality. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Mike: Count issues - learn English
Ok, I give up: I'm not going to keep repeating for Paul, or trying to determine what he's trying to say. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Second (and higher)-order methods?
On 04/30/2012 11:11 PM, Paul Kislanko wrote:
I always thought the “Condorcet is like a round-robin athletic
tournament” analogy was weak, because individual voters don’t get to go
through the round-robin and make their pairwise preferences explicit.
(As a voter, I’d find a “better/worse” pairwise choice for all pairs
easier than filling out a ranked ballot, but that just may be because
I’ve been making pairwise choices between the /ophthalmologist’s//
/lenses since I was six.) N x (N-1) “A or B” choices is an easier way to
fill out a ballot than “rank A1,A2,A3…” so no matter what method you use
to translate my ranked ballot into pairwise comparisons I have no way to
know if you counted my A<>B preferences the way I would have.
If your preferences are transitive, you don't even need N * (N-1) - O(n
log n) will suffice. Just reduce from computer sorting by having the
sorting algorithm ask you whether you prefer A to B whenever it would do
a comparison between A and B :-)
Now, I don’t think it’s a coincidence that JUST looking at PM^2 gives
the same winner (E) as Schultze does, since it’s counting the x->y->z
chains, giving extra credit to x >> z based upon x’s wins over
alternatives that themselves have {}->z wins, and that’s explicitly part
of the motivation for Schultze.
But *if* that is equivalent to Schultze (I’ll leave that test to people
who know better than I how it works) I find it more cosmetically
appealing than the Schultze definition.
I don't think it is equivalent to Schulze, because Schulze considers
paths of lengths up to the number of candidates. Instead, it sounds like
PM^2 would pick an uncovered candidate (rather like Copeland, which is
also used in sports).
If I'm right, then the Condorcet matrix corresponding to
40 D>B>C>A
30 A>B>C>D
30 C>A>D>B
should elect someone other than D. River, RP, and Schulze all elect D,
but D is covered by A.
There’s no “eliminate candidate based upon…” which has always rubbed me
the wrong way – too IRVish. All ballots and all alternatives are
directly involved in the final count.
One can describe Schulze without having to refer to eliminations, too. I
think this explanation is correct (if it isn't, Schulze, correct me):
- Candidate X beats Y if more voters prefer X to Y than vice versa. The
magnitude of this direct victory is the number of voters who prefer X to Y.
- X indirectly beats Y by a magnitude of no less than p if there exists
a sequence of candidates beginning in X and ending in Y so that every
candidate beats the one next in the sequence by at least magnitude p.
- The magnitude of X's indirect victory over Y is equal to the greatest
value of p for which the above is true. If no such sequence exists no
matter p, the magnitude of X's indirect victory is zero.
- X is a winner (or a tied winner) if no other candidate has a greater
magnitude of indirect victory against X than X has against that other
candidate.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] How would Condorcet himself have solved his paradox?
Dear Ted, I interpret Condorcet as follows: (1) Condorcet mistakenly believed that, when you successively lock the strongest pairwise defeats, then you get a linear ordering of the candidates before locking a defeat creates a directed cycle. (2) Condorcet mistakenly believed that, when you successively eliminate the weakest pairwise defeat that is in a directed cycle until there are no directed cycles anymore, then the remaining pairwise defeats always define a unique linear ordering of the candidates. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Handcounts
Here's my one cent on how votes should be recorded and counted. Two simple procedures that try to outline the basic needs. Manual approach: - representatives of multiple interest groups monitor the voting process - they check that the ballot box is empty and then seal it - voter fills the paper ballot alone in a booth - the ballot will be stamped and the voter drops the ballot in the ballot box - at the end of the day representatives of multiple interest groups open the ballot box and count the votes together on one large table right away - the summary of the local results will be agreed and published right away - all the ballots will be packed and sealed and stored for possible later additional verification right away - the content of the individual votes will not be published if their content is detailed enough to allow identification of some voters - the summary results will be sent to the central counting authority - the central counting authority sums up the results and publishes them, including the summaries of all voting locations Electronic approach: - voting machines contain a simple open source program - voting machines are stored by some central authorities - representatives of multiple interest groups open and test some of the mahines to see that they work as intended - representatives of multiple interest groups deliver the sealed machines to the voting locations - representatives of multiple interest groups monitor the voting process - they reset the voting machine - voter uses the voting machine alone in a booth - the voting machine / voting process will allow one voter to cast only one vote - at the end of the day representatives of the multiple interest groups get the summary of the votes from the voting machine - the summary of the local results will be published right away - the content of the individual votes will be erased right away, or alternatively the individual votes are strored within the sealed voting machine or printed and sealed and stored right away for possible later additional verification - the content of the individual votes will not be published if their content is detailed enough to allow identification of some voters - the summary results will be sent to the central counting authority - the central counting authority sums up the results and publishes them, including the summaries of all voting locations - if the voting machines still contain the secret individual votes they are stored locally for possible recounts for a while, or alternatively they will be delivered back to the central authorities (maybe by representatives of multiple interest groups) Hybrid approaches are possible too. Voting in the net would require some more additional security measures. On 1.5.2012, at 4.52, Paul Kislanko wrote: > As I wrote earlier, the solution to "rigged" vote-counting computers is to > make the input available to independent vote-counters like you and me, so we > can run our independently-developed implementations of the same algorithm. > > > -Original Message- > From: Dave Ketchum [mailto:da...@clarityconnect.com] > Sent: Monday, April 30, 2012 5:55 PM > To: Paul Kislanko > Cc: 'Kristofer Munsterhjelm'; election-meth...@electorama.com > Subject: Re: [EM] Dave Ketchum: Handcounts > > On Apr 30, 2012, at 7:02 PM, Paul Kislanko wrote: >> On 04/29/2012 04:48 AM, Dave Ketchum wrote: >>> Computers do well at performing the tasks they are properly told to >>> perform - better than humans given the same directions. Thus it would >>> make sense to direct the computers and expect them to do what is >>> needed accurately. >>> >>> Still, we sometimes wonder exactly what the computers have been told >>> to >> do. >> >> In my original suggestion THAT aspect of "verifiability" is covered by >> the notion that if all ballots are made a public record, independent >> programmers could perform whatever algorithm is the counting-method >> against the input. >> If 1000 members of EM (or one media outlet like CNN) got a different >> result than the vote-counting authority published, we'd know there was >> a counting error in the "official" computer code. And that would >> happen within minutes, not weeks. >> > Automatically trusting CNN, or any other single source, with automatic > credit for being more dependable than an official authority program is > stretching it. > > As I wrote earlier, a program can be rigged to give either a correct or a > biased result, as cued, with existence of the cue being hidden from > observers. > > > > Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
