At 6:59 AM -0700 5/25/06, Alex Small wrote: >I've heard that there are multiple monotonicity definitions out >there. Can somebody point me to a reference that discusses the >definition that I'm using, or perhaps one that carefully >distinguishes the definitions (so that I can sharpen the definition >in the paper)?
Voting matters has several useful papers on the subject. Three of them are Woodall's: http://www.mcdougall.org.uk/VM/MAIN.HTM 2. Properties of Preferential Election Rules Issue 3, p8-15 3. Monotonicity - An In-Depth Study of One Example Issue 4, p5-7 4. Monotonicity and Single-Seat Election Rules Issue 6, p9-14 There's a short note by David Hill on the ambiguity of the term: http://www.mcdougall.org.uk/VM/ISSUE18/I18P1.PDF The relevant portion: >Schulze [1] explains a method for single seat elections that finds >the Condorcet winner if there is one, and has a strategy for >choosing a winner where there is a Condorcet paradox. He claims that >the method is "monotonic and clone-independent". > >The main purpose of this note is to warn others who may have been >misled, as I was myself at first, by that claim. The trouble lies in >definitions, because I am told that his usage of 'monotonic' is as >normally used in the social choice literature, but it is a much >narrower definition than is often taken as the meaning in electoral >reform literature. > >He gives an example where his method certainly violates the >condition that Woodall [2] calls mono-add-top: "A candidate x should >not be harmed if further ballots are added that have x top (and are >otherwise arbitrary)", but Schulze is only claiming to meet >mono-raise: "A candidate x should not be harmed if x is raised on >some ballots without changing the orders of the other candidates". > >I am not seeking to cast any blame. If that usage of the word is >widely employed, he is fully entitled to follow it, but a clash of >definitions may cause misunderstanding if we do not take great >care.It is not my purpose in this note to examine the relative >merits, or lack of merits, of these two systems, but only to warn >that they are very different, and that the name AV is, >unfortunately, being used for both of them. Again, this may cause >misunderstanding if we do not take great care. -- /Jonathan Lundell. ---- election-methods mailing list - see http://electorama.com/em for list info
