[EM] Monotonicity Reference?

[Jonathan Lundell]

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.