[EM] Improvement to Ranked Robin method

[Richard, the VoteFair guy]

On 4/4/2022 3:49 AM, Kristofer Munsterhjelm wrote:
 > Could you give an example without truncation or equal rank, where your
 > count elects a different candidate than the Borda count restricted to
 > the same candidates?

The big weakness of the Borda count is that many voters choose to mark 
their ballot using "equal ranks" (multiple candidates ranked at the same 
level) and truncated ballots.

If, somehow, all voters can be forced to rank each candidate at a 
different rank, and assuming the number of ranks equals the number of 
candidates, then the Borda count produces very nice results.

In other words, your constraints rule out the very reason I'm suggesting 
the switch from Borda count to pairwise support counts (for the Ranked 
Robin method).

If you want evidence that pairwise support/opposition counts are better 
than the Borda count (without marking constraints), then here's a link 
to the scatter plot that shows Instant Pairwise Elimination (IPE) and 
Borda count having significantly different failure rates for CI (clone 
independence) and IIA (independence of irrelevant alternatives):

https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg

In a general way IPE is an upside-down version of the improved version 
of Ranked Robin that I'm suggesting.

IPE eliminates pairwise losing candidates when they occur during the 
elimination rounds, and otherwise eliminates the candidate with the 
highest pairwise opposition count.

In contrast, the Ranked Robin method finds the Copeland winner and uses 
as the tiebreaker the Borda count among the tied candidates.

I'm suggesting a different tiebreaker, namely the tied candidate with 
the largest pairwise support count.  This is the change that avoids the 
Borda-count vulnerability to tactical voting.

Richard Fobes
The VoteFair guy


On 4/4/2022 3:49 AM, Kristofer Munsterhjelm wrote:
> On 03.04.2022 06:24, Richard, the VoteFair guy wrote:
>> On 4/1/2022 12:04 AM, Colin Champion wrote:
>>> Llull,Borda computes Borda scores on the entire field and
>>> elects the Llull winner with the highest Borda score.
>>>
>>> Llull//Borda simulates a Borda-count runoff between the
>>> Llull winners. This can be done using totals computed from
>>> the original ballots.
>>>
>>> When I did a big simulation last year ...
>>> ... I called Llull,Borda "Llull with a full Borda tiebreak"
>>> and Llull//Borda "Llull with a restricted Borda tiebreak" ...
>>
>> Thanks, then the current definition of the Ranked Robin method is
>> Copeland//Borda -- not Copeland,Borda.
>>
>> In contrast, I'm suggesting using pairwise support counts,
>> which are described this way:
>>
>> On one ballot the pairwise support count is the number of candidates who
>> are ranked lower than the candidate getting the support count.  These
>> counts are added across all the ballots to yield that candidate's
>> pairwise support count.
>>
>> A big advantage of this method is that there is no need to teach voters
>> about pairwise vote counting beyond the win-lose kind, namely which
>> candidate got more votes than the other candidate in the pair.
>>
>> In turn, this means there's no need to mention the pairwise matrix,
>> which is confusing to many people.
>>
>> More importantly, this improved version does not suffer from the ability
>> to vote tactically, which is a big weakness of the Borda Count.
>
> Could you give an example without truncation or equal rank, where your
> count elects a different candidate than the Borda count restricted to
> the same candidates?
>
> If the outcomes are the same then I don't think your count would be any
> less (or more) strategically vulnerable than the Borda count.
>
> -km
>