[EM] XA

[Michael Ossipoff]

XA beats MJ at its own game.

Your answers have clarified XA for me, & made it straightforward.

At first it looked like a difficult mathematical or logical puzzle.

But it needn't, & I thank you for clarifying that.

XA needs a name that explicitly tells what it's about.

How about:

"Approve To Desired Total" (ATDT)?

That tells it, right in the name.

I agree with Rob: ATDT wasn't designed & introduced for single-winner
elections, & isn't to be recommended for them.

Forest--

You spoke of ATDT for chicken dilemma, & mentioned a Nash equilibrium.

But Approval has that Nash equilibrium too. The numbers are different, but
if seems qualitatively the same.

In ATDT, when the A voters give B a 33, they ensure that B can't win. When
the B voters give A 50, they ensure that A outpolls C.

...as in Approval, when the A voters say, "You know we're bigger. We aren't
approving B, because you should approve us, the bigger faction.". ...& the
B voters approve A.

Your suggested chicken dilemma solution for Approval is much better than
what ATDT offers, when it might not be obvious which faction is bigger:

Sincere preferrences:

35: A>B>>C
25: B>A>>C
40: C>>A=B

The A voters say:

"The best available estimate is that C has 40%. Suppose we're nearly equal:
You have 31%, & we have 29%.

" If we give you 10%, you beat C & win.

That means, our 29% each give B (10/29) of a vote.

You should do the same, each of you giving A 10/29 of a vote.

Then you give A (10/29)X31 = 10.69% in total.

10.69 + 29 =  39.69, less than your 41%. You win.

We all should share that 10/29 of a vote, in case our own candidate isn't
the larger one, & can't win with the 10% help.

Michael Ossipoff
On Nov 1, 2016 6:50 AM, "Andy Jennings" <elections at jenningsstory.com> wrote:

>
> On Mon, Oct 31, 2016 at 7:13 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> What makes XA do that more effectively than MJ? What's the main advantage
>> that distinguishes how XA does that from how MJ does it, or the results,
>> from the voters' strategic standpoint?
>
>
> Michael,
>
> As Rob said, the median is not terribly robust if the distribution of
> votes is two-peaked:
> http://www.rangevoting.org/MedianVrange.html#twopeak
> And I'm afraid many of our contentious political elections are two-peaked,
> at least in the current environment.
>
> With MJ, I like the fact that if the medians for all candidates will fall
> between B and D, then I can use the range outside that for honest
> expression.  Yet in the back of my head, I know that if everyone tries to
> "use the range outside that for honest expression", then the medians won't
> be in that range anymore and it seems like a slippery slope to everyone
> using only the two extreme grades.
>
> XA solves this problem by making the more extreme grades more difficult to
> achieve.  As Rob said, in the case where everyone grades at the extremes,
> the XA will match the mean.
>
> On the other hand, I admit that:
> 1) with the median, 50% would have to give the top grade for a candidate
> to receive that grade.  And 50% would have to give the bottom grade for a
> candidate to receive that grade.  I consider both of these very unlikely.
> 2) MJ is not just "the median", it has a tie-breaking scheme which
> mitigates this somewhat.
>
> ~ Andy
>
>
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