election-methods@mailman.electorama.com

Technical discussion of election methods

View all threads

Finally - the best Ranked Pairs/fpA-fpC hybrid I've found

FE
Filip Ejlak
Wed, Oct 4, 2023 11:53 AM

I've been looking for an RP/fpA-fpC hybrid that would behave properly in
all circumstances (Selective RP had some bad edge cases) and I believe I've
finally found it.

Here's the shortest definition:

Iteratively restrict the set of candidates to all candidates X such that
for some XYZ contest:

- the Ranked Pairs winner is the same as for all current candidates
- the fpA-fpC winner is X
until there's only 1 candidate left.

That's it. The logic behind it is quite simple - either we find buried DMT
candidates (and we choose among them) or we choose the current RP winner.

Here's the set of criteria I was looking for:

  • cloneproofness
  • monotonicity
  • ISDA
  • DMTBR
  • preferably: LIIA

The simulations indicate that this method satisfies all of that, with no
special tie-breaking rules needed. It indeed seems to have overall strategy
resistance on Smith//IRV level. But, as always, I will be thankful for any
independent checks.

(I'm not sure about the name yet. Burial-Detecting Ranked Pairs?)

I've been looking for an RP/fpA-fpC hybrid that would behave properly in all circumstances (Selective RP had some bad edge cases) and I believe I've finally found it. Here's the shortest definition: *Iteratively restrict the set of candidates to all candidates X such that for some XYZ contest:* *- the Ranked Pairs winner is the same as for all current candidates* *- the fpA-fpC winner is X* *until there's only 1 candidate left.* That's it. The logic behind it is quite simple - either we find buried DMT candidates (and we choose among them) or we choose the current RP winner. Here's the set of criteria I was looking for: - cloneproofness - monotonicity - ISDA - DMTBR - preferably: LIIA The simulations indicate that this method satisfies all of that, with no special tie-breaking rules needed. It indeed seems to have overall strategy resistance on Smith//IRV level. But, as always, I will be thankful for any independent checks. (I'm not sure about the name yet. Burial-Detecting Ranked Pairs?)
KM
Kristofer Munsterhjelm
Wed, Oct 4, 2023 10:30 PM

On 10/4/23 13:53, Filip Ejlak wrote:

I've been looking for an RP/fpA-fpC hybrid that would behave properly in
all circumstances (Selective RP had some bad edge cases) and I believe
I've finally found it.

Here's the shortest definition:

/Iteratively restrict the set of candidates to all candidates X such
that for some XYZ contest:/

/- the Ranked Pairs winner is the same as for all current candidates/
/- the fpA-fpC winner is X/
/until there's only 1 candidate left./

That's it. The logic behind it is quite simple - either we find buried
DMT candidates (and we choose among them) or we choose the current RP
winner.

I'm not quite sure what you mean by iteratively restricting the set.
Could you give me an example of how the method works? Say, Schulze's
five candidate example:

5: A>C>B>E>D
5: A>D>E>C>B
8: B>E>D>A>C
3: C>A>B>E>D
7: C>A>E>B>D
2: C>B>A>D>E
7: D>C>E>B>A
8: E>B>A>D>C

if it wouldn't be too tedious? It's got a large Smith set.

-km

On 10/4/23 13:53, Filip Ejlak wrote: > I've been looking for an RP/fpA-fpC hybrid that would behave properly in > all circumstances (Selective RP had some bad edge cases) and I believe > I've finally found it. > > Here's the shortest definition: > > */Iteratively restrict the set of candidates to all candidates X such > that for some XYZ contest:/* > */- the Ranked Pairs winner is the same as for all current candidates/* > */- the fpA-fpC winner is X/* > */until there's only 1 candidate left./* > > That's it. The logic behind it is quite simple - either we find buried > DMT candidates (and we choose among them) or we choose the current RP > winner. I'm not quite sure what you mean by iteratively restricting the set. Could you give me an example of how the method works? Say, Schulze's five candidate example: 5: A>C>B>E>D 5: A>D>E>C>B 8: B>E>D>A>C 3: C>A>B>E>D 7: C>A>E>B>D 2: C>B>A>D>E 7: D>C>E>B>A 8: E>B>A>D>C if it wouldn't be too tedious? It's got a large Smith set. -km