1. Condorcet Enhancement (Forest Simmons)
2. Re: Condorcet Enhancement (Magos?nyi ?rp?d)
3. Re: Condorcet Enhancement (Abd ul-Rahman Lomax)

By Chicken Resistant I mean satisfying the Chicken Dilemma Criterion. See https://electowiki.org/wiki/Chicken_Dilemma_Criterion Since I posted this Condorcet Enhancement technique, while working on the proof of monotonicity I realized that more is required of the base method than mere monotonicity. Satisfaction of the FBC by the base method is sufficient to preserve monotonicity in the enhanced method. Otherwise, the attempted proof breaks down because raising the enhanced winner W' relative to the other candidates could change the base method winner from W to some W'' not in the set of candidates that flow into W' in the directed graph. If the method satisfies the Favorite Betrayal Criterion, then raising W' in the base method leaves the new base winner in the set {W, W'} which is contained in the set of vertices that drain into W', since candidate W' is by definition the final destination of W in the flow of the digraph. So enhanced MMPO (MinMaxPairwiseOpposition), enhanced Equal Rank Whole and rated versions of Bucklin (including Majority Judgment), enhanced Borda, enhanced Plurality, enhanced Range (including enhanced approval), enhanced Random Ballot, and some versions of enhanced asset voting, will all be monotone from start to finish. When using cardinal ratings (i.e. grades, scores, or range style ballots) we can improve upon the directed graph as follows: If X is covered, draw an arrow from X to the candidate Y (from among those that cover X) that incurs the least total disappointment in the transition from X to Y. The disappointment incurred on a given ballot is zero if Y is rated above X on that ballot, otherwise it is the difference in the rating of X and the rating of Y on that ballot. The total disappointment is the sum over all ballots of the ballot disappointments. If we use the resulting digraph in our Condorcet enhancement, we produce a Condorcet method that respects the expressed ratings of the voters beyond the utility contribution from the base method. In other words when the enhancement phase is based on mere rankings, some of the utility flavor of the base phase may be lost. On Mon, May 20, 2019 at 10:43 AM < election-methods-request@lists.electorama.com> wrote: > Send Election-Methods mailing list submissions to > election-methods@lists.electorama.com > > To subscribe or unsubscribe via the World Wide Web, visit > > http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com > > or, via email, send a message with subject or body 'help' to > election-methods-request@lists.electorama.com > > You can reach the person managing the list at > election-methods-owner@lists.electorama.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Election-Methods digest..." > > > Today's Topics: > > 1. Condorcet Enhancement (Forest Simmons) > 2. Re: Condorcet Enhancement (Magos?nyi ?rp?d) > 3. Re: Condorcet Enhancement (Abd ul-Rahman Lomax) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 19 May 2019 16:10:17 -0700 > From: Forest Simmons <fsimmons@pcc.edu> > To: EM <election-methods@lists.electorama.com> > Subject: [EM] Condorcet Enhancement > Message-ID: > <CAP29oncLAXha=7kX2iQexe8oSNCkOSti4Z+1BOOrPvnfhuem= > Q@mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > There are various ways to enhance a given method to make it Condorcet > compliant: > > 1. One can elect the ballot CW if there is one, and otherwise fall back on > the given method. > > 2. One can apply the given method to the Smith set. > > 3. One can use the given method winner as the starting point in a seamless > process that leads to a member of the Smith Set (or better). > > Here is such a process: > > First, create a directed graph whose vertices are the candidate names as > follows: > > For each covered candidate X, draw an arrow to that candidate Y (among > those that cover X) which is ranked or rated strictly below X on the fewest > number of ballots. > > To enhance the winner A of any method, start at candidate A and follow the > arrows as far as possible in the directed graph. The enhanced winner W' is > the one at the end of the directed path. > > This W' covers W, but is itself uncovered (a member of the Landau Set), and > so also a member of Smith. > > If the original method elects monotonically, then so does the enhanced > method. > > If the original method satisfies the FBC or in any case lacks vulnerability > to compromise, then the enhanced method gives little incentive for burying > Favorite because when there is an arrow from Favorite to Y, candidate Y is > already the natural compromise candidate for the supporters of Favorite, > the one that is rated strictly below Favorite on the fewest ballots among > those that cover Favorite. > > Suggestions: > > A. Enhanced Approval. > B. Enhanced Majority Judgment > C. Enhanced Random Ballot > D. Enhanced Asset Voting (different possible versions) > E. Enhanced Chiastic Approval > > Other versions? > > If method M is Chicken Resistant, does it follow that the Enhanced version > of Method M also Chicken Resistant? > > Other thoughts? >