Voting Scene Theory

Foreword

This is a new field of mathematics that intersects voting theory, discrete math, and cinematography. It answers the following question:

In a TV show or movie scene that wants to be dramatic for a scene to ty and optimize the entertainment of the audience…

There are P participants who voted for a discrete-choice poll (election) with K choices and their votes are revealed in a certain way F, how do you optimize the entertainment value extracted from that given vote reveal scene?

Summary

Let’s say you had to write a scene in a TV show where 5 characters vote for a yes or no decision.

What’s the most exciting, surprising way to structure revealing the votes one by one so the audience is both surprised and satisfied with the results?

Initiating the vote

In some situations, a group might not be wanting to vote, so the vote that initiates the vote could be perceived as the favorites going in.

Ending the vote

The vote can either end when all five votes have been revealed, or when it’s mathematically impossible for revealing a vote to affect the outcome of the result.

Obviously, having leftover votes not be shown is a waste of dramatic real estate.

Example: 5 Votes, 2 Options

If a result leads with Y then there’s already some assumed bias that Y is going to win. (Without loss of generality, swap Y and N)

The result that leads with Y is likely a-priori the vote that the majority of people think is going to be the result based on their estimates of how everyone will vote.

1. Y N , , ,

Predictable. The most egalitarian way to start.

1.a Y N Y , ,

yawn Boring! Too fair!

1.a.i Y N Y Y ,

Whoa! Wait, that was unexpected! This definitely feels like a surprise in execution, but is not very satisfying in terms of the voting.

1.a.ii Y N Y N ,

Okay, this feels like the first four didn’t even matter and we could’ve held a vote with just one person.

1.a.ii.A Y N Y N Y

This feels like a waste of time! Why put it up to a vote if the person calling the vote could’ve singlehadedly decided for us? Also, it’s just an alternating pattern

1.a.ii.B Y N Y N N

Wait a second. Whoa. This is trippy. Not only did we break an alternating pattern, we introduced two-in–row at the end instead of the beginning!

2. Y Y , , ,

OK, what I’m really going to be watching is “where are they putting the Y”, where the options shrink every time they reveal. So the excitement curve is already biased way low.

2.a. Y Y Y , ,

This is the least surprising voting sequence, perhaps even zero-surprise-units.. By vote 3, the result is mathematically sealed. Votes that are completely random where all the characters vote without any knowledge is, obviously, not entertaining

2.b. Y Y N . .

This is the best way start to a scene.

2.b.i Y Y N N .

This is exciting. It’s anybody’s game.

2.b.i.A Y Y N N N

Aaand now it feels unsatisfying to have three of the same votes in a row. I mean,, what are the odds of that happening? As humans, we are biased against votes that look “sorted” and so “unfair”.

2.b.i.B Y Y N N Y

This is absolutely brilliant. Subversive. Letting the vote that started get the win, even though they cockily took the first two in a row? Beautiful.

2.b.ii Y Y N Y .

Very subversive. After the results of vote 2.b, you might have lead the audience to believe it was going to be set up as Y Y N N Y or Y Y N N N, one of which is the most satisfying result.

Generalizations

• Alternating patterns are not exciting if the viewer is paying attention to them, and the end result feels expected.
• Breaking alternating patterns is very exciting.
• Randomness is exciting.

Future Investigation

This post dealt with when the results are shown one-by-one.

A future analysis could consider non-linear ways to determine the number of votes to reveal at a given time. Like what if one was revealed as Y, two was revealed as N, but then three-five are all revealed at once as Y?

What about votes with a number other than 5? You fool. Half of those are useless, because votes among 4 can tie! Votes among even numbers of people that can tie are EVEN WORSE to watch!

This idea could be formalized with math. A voting scene could be represented by a finite series of choices S_n and then we can measure the randomness and the satisfaction level.

Randomness of a series can be measured with a randomness test, while satisfaction level is more subjective.