# [EM] Markus--You didn't prove that ERIRV(fractional) fails WDSC

James Green-Armytage jarmyta at antioch-college.edu
Wed May 4 23:16:45 PDT 2005

```Mike, you wrote:
>The example that was linked to, intended to show that ERIRV(fractional)
>fails WDSC doesn't show that.
>So, so far no one has posted an example of ERIRV(fractional) failing WDSC.
>I've just now looked at the e-mail, and so I haven't yet had the
>opportunity
>to check out James's demonstration that ERIRV(fractional) passes WDSC.

In light of Markus's example, I think that my proof only works for 3
candidate cases. (That is, step 11 is incorrect.)

>, But
>I post this message now, because it's obvious that the 5-candidate 119
>voter
>example does not show that ERIRV(fractional) fails WDSC.
>Markus' example might show that it's possible for people to vote in a way
>that elects E. But that isn't what WDSC talks about. The question is: Is
>there a way that those 60 A>E voters could vote that would ensure that E
>won't win, without them having to reverse a preference?
>Should we assume that Markus' rankings in that example represent
>preferences
>What if those 60 voters ranked equally A and everyone whom they prefer to
>A?
>There isn't time to check that out right now.

Markus's example seems to demonstrate that ER-IRV(fractional) fails WDSC
when altered as below.
A majority (60 out of 119) ranks A as tied for first, and E as tied for
last. I believe that E wins.
I'm not sure what is the practical significance of the failure, if all
failure examples need to be as heavily contrived as this one.

10: B=C=A>E=D
10: B=D=A>E=C
10: C=B=A>E=D
10: C=D=A>E=B
10: D=B=A>E=C
10: D=C=A>E=B
7: B>E
7: C>E
7: D>E
38: E

ER-IRV(fractional) tally:
A		B		C		D		E
20		20.33		20.33		20.33		38
-20		+6.67		+6.67		+6.67
27		27		27		38
-27		+10		+10		+7
37		37		45
-37		+20		+17
57		62

Hopefully I didn't make errors in the tally (it's a bit tricky). You
should do it yourself to be sure.

Sincerely,
James

```