Dear all, It seems to be the case that the prevailing opinion on this list is, that Condorcet methods violate the favorite betrayal criterion (FBC). Is that correct? I have looked for a while in the archives election-methods list for an example of the FBC violation for Condorcet methods, but didn't find any. Maybe I didn't look deep enough. FBC is not listed on Wikipedia with the other criteria, so it seems that this criterion is at a "pre-scientific" stage of formulation, correct? There is no example on the electrorama wiki either. So I thought I'll turn to the experts on this list for some quick help in this area. Personally I think that Condorcet methods (take Schulze as reference) with symmetrical ballot completion might satisfy FBC, but I am not sure, so that's why I ask for some guidance here.
In order to avoid misunderstandings, below I: A] first provide the relevant definitions, B] then give questions for FBC violation examples and C] finally specify how the examples of FBC violations should (could?) look like in order to avoid misunderstandings. A] DEFINITIONS (Alex Small): https://sites.google.com/site/physicistatlarge/FBC_latest.pdf?attredirects=0 1. FBC: A voting method satisfies the Favorite Betrayal Criterion (FBC) if there do not exist situations where a voter is only able to obtain a more preferred outcome (i.e. the election of a candidate that he or she prefers to the current winner) by insincerely listing another candidate ahead of his or her sincere favorite. 2. SFBC: A voting method satisfies the Strong Favorite Betrayal Criterion (SFBC) if there do not exist situations where a voter is only able to obtain a more preferred outcome (i.e. the election of a candidate that he or she prefers to the current winner) by insincerely listing another candidate ahead of or equal to his or her sincere favorite. 3. Generalized symmetrical completion is defined as follows: (i) equalities between candidates on the ballot (A=B) are resolved as 0.5 votes for each candidate in the pairwise comparison. (ii) Ballots are completed with the null candidate ("none of the above" X), who is ranked strictly lower than all candidates explicitly ranked on the ballot, (iii) candidates not explicitly ranked on the ballot (i.e. truncated ballots, excluding the null candidate) are ranked equally below the null candidate. Example: election with candidates A, B C, the bullet-vote ballot A is completed as A>X>B=C, A>B>C is completed as A>B>C>X). B] QUESTIONS QUESTION 1. Do you know of an example which shows that FBC or SFBC is violated for Condorcet elections (reference method Schulze) where ballots are completed using generalized symmetrical completion? QUESTION 1. Do you know of an example which shows that FBC or SFBC is violated for other types of Condorcet elections (reference method Schulze), than those where generalized symmetrical completion is used? C] SPECIFICATIONS OF EXAMPLES In order to avoid misunderstandings, please send your examples on the following form. Please submit two elections on the standard form (i.e. number of voters for each distinct type of ranked ballot, equally ranked ballots allowed) In the first election some voters C give the first preference to a candidate A. An other candidate than A wins the election In the second election A wins the election and some of the voters in group C give A a second preference or less (FBC) or give an other candidate a shared first preference with A (i.e. A=B is the shared first preference) (SFBC). No other changes occur, i.e. all other rankings in group C and outside group C remain unchanged from the first election. I assert for the sake of argument, that FBC is satisfied for Condorcet methods (at least Schulze) when generalized symmetrical completion is used. Please show me wrong :o) If there is something I haven't understood, please give some advice. I am a newbie on this list, so things are a bit new to me here. Thanks. Best regards Peter Zborník ---- Election-Methods mailing list - see http://electorama.com/em for list info
