# [EM] STAR Voting Variations

Susan Simmons suzerainsimmons at outlook.com
Mon Jul 12 18:41:22 PDT 2021

```... continuing ...

Here's another small tweak to create a similar, but much improved method ... let's call this tweak of STAR, "CHAMP."

STAR elects the pairwise winner between the score winner X and the candidate Y  who is the score winner among the other candidates (besides X).

CHAMP elects the pairwise winner between the score winner X and the candidate Z who is CHAMP winner among the other candidates (besides X).

Both methods pit the score winner against a runner-up from among the other candidates (besides the score winner).

In STAR the method for choosing the runnerup is score (restricted to the other candidates) which simply yields Y, the candidate with the second highest score over-all.

In CHAMP the method for choosing the runner-up is CHAMP itself (restricted to the other candidates).

[At first glance this looks like a case of circular definition, but in mathematics definitions of this form can (under certain conditions satisfied in this context) be considered as logically convergent spirals called "recursions," rather than circles.]

It turns out that this description of CHAMP is just a particularly compact [and elegant, in the eyes of software engineers] reformulation of Sequential Pairwise Elimination (SPE) applied to the "agenda" of candidates listed from least to greatest scores.

SPE is a highly respected method that has been used in many kinds of deliberative bodies for centuries, and recommended by "Robert's Rules of Order" for choosing from among more than two options ... two-at-a time from an agenda with the least promising agenda items listed first. In the CHAMP context "least promising" means lowest score.

CHAMP is clone proof, monotonic, and Condorcet compliant ... what simpler method has this much going for it?

...   to be continued ...

Sent from my MetroPCS 4G LTE Android Device

-------- Original message --------
From: Susan Simmons <suzerainsimmons at outlook.com>
Date: 7/10/21 5:55 PM (GMT-08:00)
Cc: election-methods at lists.electorama.com
Subject: STAR Voting Variations

STAR is a great gateway method because there are so many different directions to tweak/elaborate/improve/generalize it to transform it into other simple methods based on similar ideas.

For example, Majority Judgement Top Two Runoff, that uses the exact same score ballots, voted exactly the same.

While STAR pits against each other the two candidates with the greatest average ("mean") scores, MJTTR compairs the two with the greatest median scores.

Why median instead of mean? Because use of the median gives less strategic incentive for voting closer to the extremes, and the un-exagerated ratings of MJ voters makes the pairwise comparisons more accurate due to fewer strategy induced tied ballot ratings.

Majority Judgement is a score based version of Bucklin that has an ingenious way of breaking the median ties that are extremely likely, as anyone used to dealing with medians will understand.

Why do medians discourage exageration? Suppose the median score for candidate X is three, then changing any ballot rating above three to another one above three would make no difference ... same for ratings below three: the median is less rewarding to exagerating manipulators.

Experiments by the MJ inventors seem to support the idea that voters under MJ experience little to no temptation for exagerating their best honest estimates for the deserved ratings of the candidates.

That said, there is another metric called "chiastic approval" that is a very nice compromise between mean and median ballot ratings ... which we will come back to in the future, after considering more of the low hanging fruit in another direction ... (to be continued)

Sent from my MetroPCS 4G LTE Android Device

-------- Original message --------
From: Susan Simmons <suzerainsimmons at outlook.com>
Date: 7/8/21 9:04 PM (GMT-08:00)
To: Daniel Carrera <dcarrera at gmail.com>
Cc: election-methods at lists.electorama.com
Subject: Re: [EM] STAR Voting

BTW its not just the clone thing that makes me think that STAR is strategically equivalent to Approval, rather it is the combination of these two facts:

(1) Score Voting is strategically equivalent to Approval ... optimal strategy entails voting at the extremes (mostly if not exclusively).

(2) If voters vote only at the extremes, the Score winner will be the pairwise winner of every head-to-head contest.

So in the case of sophisticated voters the top two runoff is redundant.

For naive voters it is harmless and may serve some valuable psychological purpose.
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