[EM] Strategy-free criterion

[Chris Benham]

Kevin,

> MD basically says that if there are two frontrunners and everyone truncates their
> less liked frontrunner, then the worse frontrunner won't win. If this property
> doesn't hold, it means the majority has done something to stop the method from
> "seeing" their majority, which is surely that they ranked other candidates above
> the preferred frontrunner.

Instead of "above the preferred frontrunner" don't you mean *below the 
less-liked frontrunner*?

The classic example used by people who like Winning Votes and Approval 
to flout those method's compliance with MD (versus the MD failures of 
Margins and IRV):

49 A (sincere might be A>B)
24 B  (sincere might be B>C)
27 C>B (sincere)

A>C  49-27 (=23)     C>B  27-24  (=3)    B>A  51-49  (=2)

By Margins A's defeat is the weakest and MinMax (and methods that are 
equivalent to it with only 3 candidates, such as Ranked Pairs and 
Schulze) using margins elects A.

But Minimal Defense says "not A" because more than half the voters voted 
B above A and A not above equal-bottom.  MD has no problem with the 27 
C>B voters who ranked a candidate above their preferred (presumably 
perceived) "frontrunner."

What you wrote seems to better apply to another criterion about voters 
"defending the (presumed) sincere CW",  Steve Eppley's "Non-Drastic 
Defense" that says that if more than half the voters rank X above Y and 
X no lower than equal-top then Y can't win.

I think this was his example:

46 A>C  (sincere is A>B)
17 B>A  (sincere)
17 B>C  (sincere)
20 C=B  (sincere is C>B)

A>C  63-37 (=26)     C>B 46-34 (=12)    B>A 54-46 (=8)

More than half the voters have voted B above A and B no lower than 
equal-top and so NDD says that A can't win, but Margins elects A. 
Winning Votes meets NDD and elects B.

Chris B.


On 2/06/2024 7:23 am, Kevin Venzke wrote:
> Hi all,
>
> When I test for SFC compliance the rule on cast votes is that if there is no
> majority over A, and A has a majority over B, then B can't win.
>
> This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
> in terms of a graph of majority-strength defeats, it would say that if A has a
> majority over B and B doesn't have a majority over anyone, then B can't win.
>
> MD basically says that if there are two frontrunners and everyone truncates their
> less liked frontrunner, then the worse frontrunner won't win. If this property
> doesn't hold, it means the majority has done something to stop the method from
> "seeing" their majority, which is surely that they ranked other candidates above
> the preferred frontrunner. So MD is mostly about compromise incentive.
>
> SFC is probably going to be about truncation. When a method fails it, most likely
> it's because the majority gave the election away to a less liked compromise choice.
> For example:
>
> 20 C>A>B
> 35 A>B
> 5 B
> 40 D
>
> Here B is the implicit approval winner, but by SFC B should not win, because it
> means it was not safe for the A voters to rank B.
>
> I would not like to see SFC as totally obsolete, since it was one of the motivating
> criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
>
> Kevin
> votingmethods.net