## Range Voting strategy, and DYN, a proposed new voting method

by Forest W. Simmons (PhD)

### Part I.

Suppose that an election is being conducted under Range Voting and that you want to maximize the probability that your ballot will improve the outcome of the election, i.e. the probability that your ballot will be "positively pivotal."

If this is your goal, then your optimal strategy requires you to rate all of the candidates at the two extremes of the range.

At which extreme should candidate X be rated? To answer that question, first answer this one:

If X were to be tied for the highest average rating, would it be more likely for X to be tied with a worse candidate or with a better candidate?

If worse, then give X the maximum rating. If better, then give X the minimum rating.
[Actually, this decision should really be based on expected utility, but this point will not matter for our purposes.]

With this type of strategy the intermediate ratings are superfluous.

If all voters are planning to use this kind of strategy, then the ballot can be vastly simplified by using a two-value range, say YES versus NO. Then we just have Approval Voting.

The trouble with Approval Voting is that optimal Approval strategies depend heavily on knowing the probabilities of wins and ties for the various candidates as in the strategy discussed above.

These probabilities are hard to estimate, and it's easy for evil corporate media-masters to distort those estimates, thus biasing everybody's strategizing, thus biasing the voting, thus getting whomever they want elected, thus bypassing democracy.

What is the solution?

A variation of Approval called DYN (for "Delegable Yes/No"), which I will explain in Part II.

(Take a break.)

### Part II.

In part I above we had good and bad news for Range voters:

Good news:
To maximize the probability that your Range ballot will improve the outcome of an election (relative to the outcome without your ballot), you only need to vote at the range extremes. If all Range voters want to do this, then a simple Yes/No approval style ballot suffices.

Furthermore, under Range and Approval it can never hurt to rate your favorite candidate at the positive extreme. This last advantage is not shared by Borda, by any Condorcet method, or by any sequential elimination method, like IRV. In all of those other methods it can actually hurt you to rank your favorite candidate top in crucial cases that arise with non-vanishing likelihood.
Disinformation about winning probabilities can easily thwart optimal Approval strategy (and therefore, Range Voting strategy). In other words, like strategic voters in all of the other well known methods, Range/Approval voters are (to at least some degree) subject to manipulation by disinformation from pollsters.

The simplest solution to this problem that doesn't compromise the "always give maximum support to favorite" advantage that Approval and Range share over the other common methods is a variant of Approval known as DYN, which stands for Delegable Yes/No:

 Each voter marks "YES" next to all of the names on the ballot that she is sure that she wants to rate at the positive extreme, and "NO" next to all of the names that she is sure she wants to rate at the negative extreme. She also may leave some candidates blank (neither YES nor NO). Then she circles the name of a candidate (presumably her favorite) to act on her behalf with regard to her unmarked choices. [If she does not so designate any candidate, then any unmarked names will default to "NO."] She has been given to understand that her designated candidate will make the delegated decisions after all of the ballot sub-totals have been made public. All the votes are totaled. At this point, there is some known number of YES votes for each candidate. But wait – there is more. Say it is a C-candidate election. Each candidate also has C-1 "bank accounts" (one for each of his rivals) consisting of blank votes under his control for that rival. If candidate "Lincoln" has 57 votes in his bank account for rival "Douglas" then he is now free to label those votes as either "YES" or "NO" for Douglas. After all the candidates have thus-labeled their delegated-votes, whoever now has the most YES votes, wins.

Advantage: Unmanipulable by evil pollsters: The results available at stage 3 (e.g. proxy tallies, already-decided Yes/No tallies, relevant correlation coefficients, etc.) serve as a reliable statistical basis for candidates (with help from trusted technical advisers) to carry out their proxy obligations. They won't have to (or want to) rely on guessy poll results because with this information, they've got the ultimate truth. This will greatly mitigate (if not totally nullify) the effects of any disinformation spread by (official or unofficial) pollsters.

DYN can be viewed as a variant of approval voting. And as with plain approval, approving your favorite can never hurt.

DYN has another advantage over plain Approval and Range. By designating your favorite candidate to complete the Yes/No decisions that you are unsure about (and/or that you don't care about) you are able to express unique confidence in your favorite candidate above and beyond the other candidates that you have supported with a rating at the positive extreme.

That gives both moral support and extra decision power to your favorite candidate.

Even if your favorite candidate does not have sufficient support to be elected himself, there is a chance that the proxy power (to which you contributed) will give him enough political leverage to improve the outcome of the election over what it would have been otherwise.

This completes Part II of my explanation of the main rationale for the creation of DYN from the point of view of a Range/Approval fan. If you weren't a "Range/Approval fan" then read part III.

### Part III.

To take this to the general public, I would place more emphasis on the ease of DYN voting as compared to ranking the candidates. Yes/No is easy – and the fact you can "pass the buck" on any candidates you are unsure about, makes it even easier. Meanwhile, ranking every candidate in order, is not easy.

I'd also give more emphasis to the importance of the Favorite Betrayal Criterion (FBC), which is failed by IRV, Condorcet (with or without ranking-equalities permitted) Borda, etc.

(On the downside, a disadvantage of DYN is that it is more complicated to count than plain approval voting and hence can't be done with dumb voting machines.)

Why do we want a new voting method? So we can give maximum support to our favorite candidate without risking turning her into a "spoiler." Since simple methods that satisfy this FBC requirement are known, no complicated method that fails it can be acceptable.

Besides Range and Approval none of the well-known methods satisfy FBC except a method called MMPO (MinMaxPairwiseOpposition) and certain versions of Bucklin, all of which require strategy similar to approval strategy, based on the same type of poll-based information. That leads to the same worries about evil media-masters feeding us disinformation. So we are led inexorably back to DYN.

For IRV supporters who think that IRV comes close enough to satisfying the FBC (even though it doesn't), our best ammunition is in the form of Yee-Bolson diagrams. These diagrams, more than anything else, have convinced my Liberal Arts Math students that IRV is inferior to Approval and Condorcet methods, and not much of an improvement on Plurality for getting third parties into the running.

The only problem with Yee-Bolson diagrams is that students need a lot of interactive help in understanding how these diagrams work and exactly what they represent. Just showing them the pictures with the explanatory material from the websites is not enough.

Who can take the bull by the horns and get the truth into the hands of the movers and shakers?