Voting Systems
January 28, 2022
Sam Schikowitz

“Together we are smarter than anyone.”

When you think about how we make decisions in our society, for example voting for president or Brexit, have you ever wondered “Really? Is this the best we can do? Even with what we think are the best processes in place, the results still don’t seem to be optimal.”

Democracy is the middle path between chaos on one hand, and authoritarian rulers on the other, where the control emerges from the will of the governed.
We should not take it for granted but we also shouldn’t think it is something fixed in stone.

There are many ways to do Democracy, and I have strong evidence to present, suggesting that the problems we are encountering in our democracies are largely due to the details of how we run things, like the voting systems we use.
If we are not happy with how things are turning out, we need to tweak the process.

In this article I want to share what I’ve discovered about our voting systems. A few areas I’ll dive into:

  1. The most commonly used Single Choice voting methods,
  2. Why they fail,
  3. Voting systems that actually make sense, (Approval voting, Ranked Choice, and Score.)
  4. I’ll talk about how these voting systems are integrated into Forby.org, the software that I’m developing to help groups collect, develop, and prioritize the ideas of its members.

Voting is a natural human behavior. Hunter gatherer tribes are known to use voting, and the first recorded system of governance to use voting was in ancient Athens around 2500 years ago. 

I’ve had the opportunity to speak with a few of the most famous mathematicians who study the science of voting, Like Richard Darlington from Cornell University, Mathematician Pietro Speroni di Fenizio, and Richard Fobes, The VoteFair guy, and according to them we are definitely doing it wrong in most democratic countries.

 What’s so wrong you might ask? Let’s dive in.

But first, before voting happens, a political system can be judged on how the crafting of ideas and proposals, and how nominating candidates happens.

A famous election rigger from the early 1900s named Boss Tweed was quoted as saying:

“I don’t care who does the electing, so long as I get to do the nominating.”

Political voting can give people a chance to feel involved, but in most countries it’s just a checkbox exercise, voting for voting sake instead of making real decisions. The options themselves are already not good. It’s a case of

 “Garbage in garbage out.”

 Having said that, once options are available, not all methods of picking a winner are equal.

 Voting systems are susceptible to various flavors of unfairness.

Let’s start with the one used for most elections in most countries, and one of the least favorite among mathematicians.

Single Choice  

Single-Choice Voting, as the name suggests, require you to pick only one of a list of options. 

Within Single Choice voting, Plurality is the simplest version where the winner is the one with the most votes, like Us, Canadian, British, and Indian legislative elections.

Another version is called Majority Rule, as in US presidential elections. The winner has to get over 50% of the votes, otherwise a contingency plan is called in.

There are 4 flavors of unfairness with **Single Choice Voting. As I explain, you will recognize how much these unfairnesses affect our political landscape:

1. Split the vote spoilers and the”Lesser of 2 Evils.”

If there are 2 options who are both loved by most voters and one that is preferred by a smaller group, the 2 popular options can “split the vote,” leaving the less popular option as the winner.

In Majority Rule voting like US presidential elections, there are always only 2 establishment options, and there is no diversity of candidates represented by 3rd party candidates. 3rd party candidates cannot be a viable option because if they win a significant number of votes, they will ether destroy the chances of the major party that they are most similar to, or, with enough votes make it impossible for any candidate to win a majority.

For this reason, in Single Choice elections, we always hear people say they’re voting for someone they don’t like because they are the “lesser-of-two-evils”.
We are all voting for someone we don’t like, and not voting for the option we really do like, because we see our favorites as unwinnable, and if we don’t our votes are wasted.

2. Winner Takes all and Wasted Votes

Because the Winner Takes All, the preferences of those who don’t vote for the winner don’t provide any information as they do in systems where voters rank or score their preferences. These wasted votes are what make gerrymandering possible, which means when a political party rearranges the districts so that their candidate has razor thin victories is most areas and major losses in a few, and hack the system in their favor.

3. The Apathy of Approving losers.

Under Plurality, many people feel that voting is an empty ritual. An option despised by most of the population can win as long as it’s approval percent is higher than the other options.

4. Mathematically bad.

Single Choice is a simple and intuitive counting system. It’s certainly the one used by ancient tribes and ancient athenians, and it’s ok mathematically when there are only 2 choices, and people must select one.

Once there are more than two options, like elections with multiple candidates, or multiple options, Single Choice systems start to fail mathematically. 

I’ll go through an example of 15 people who are asked to rank their preference for Mangoes, Strawberries, and Grapefruit.

  • Six rank them like this: 1st: Grapefruit, 2nd Mangoes, 3rd Strawberries
  • Five rank them like this: 1st: Strawberries , 2nd Mangoes, 3rd Grapefruit and
  • Four rank them like this: 1st: Mangoes , 2nd Strawberries, 3rd Grapefruit

A minority of 6 (40%) liked grapefruit the most, but most candidates, 9 out of 15, ranked it last. In a Majority Rule system, since none of the options passed 50%, a contingency would have to be called in as there is no Majority. In plurality voting the outcome is simple:

  1. Grapefruit wins with 6 out of 15, or around 40% of the vote, followed by
  2. Strawberries with 5 for 33%, with
  3. Mangoes trailing in last with 4 for 27%.

So do voters actually prefer Grapefruit?
Not at all.

Why? I’ll show you by comparing the results with each of the 3 Voting systems that actually make sense, (Approval voting, Ranked Choice, and Score.)

 Approval voting

Approval Voting has been used by Cardinals to approve the Pope since the 13th century, and by the UN to approve the Secretary General.
In this method, voters vote to approve or reject each option.

In this way, voters can vote with their conscience, approving every candidate that they believe is a viable option.

This makes it good for moderate candidates who appeal to both left and right.

The option with the most Approvals is the winner, and if needed the election can select a number of winners.

 

It shows:

  1. All of the candidates who got enough approval to pass, and
  2. The rank of approval, from first to last.

Approval voting is also handy when choosing many options, such as what plants to plant in a family garden.

 

In our fruit example, let’s assume the voters approve their first two choices and reject the third option:

  • Six approve Grapefruit and Mangoes, and reject Strawberries
  • Five approve Strawberries and Mangoes and reject Grapefruit and
  • Four approve Mangoes and Strawberries and reject Grapefruit

That’s

  1. Grapefruit: 6 approvals,
  2. Strawberries: 9 approvals, and
  3. Mangoes: Unanimously approved with 15 votes!

The exact reverse of what the Single Choice voting system produced.

If grapefruit had won, 9 of the 15 voters would have been unhappy. Sound familiar?

 

On the other hand, the risk of approval voting is that people may choose to reject all but their favorite, gambling that the strength of their preference for their first choice is worth sacrificing the chances for their second or third choices.

 

While this is not ideal, the gain made by strategic voting is not much and puts a voter’s secondary preferences at risk.

 

In the worst case scenario, we are back to Single Choice voting, and in most scenarios, more people are happy with the choice.

 Ranked Choice

Also known as Condorcet Voting or Pairwise Method, Ranked Choice is calculated by looking at pairs, like Grapefruit vs. Mangoes, to see how many voters preferred each fruit against each other fruit.
Variations of Ranked Choice are used in Australia, Ireland, New Zealand, Malta, Northern Ireland, and Scotland.

This method was developed during the French revolution and is a little more complicated mathematically.

Ranked Choice gathers a lot of information about voter preferences, and so it tends to find more centrist options that most people approve of, It is less able to be manipulated than any of the other options.
It is the ideal option for large public elections.

So back to our fruit example:

  • When you remove mangos and only compare grapefruit with Strawberries, you see that 6 (40%) prefer grapefruit and (5+4), or Nine of the 15 voters (60%) prefer Strawberries to Grapefruit, and
  • When you remove strawberries, you see that 60% also prefer mangos to Grapefruit.

Clear majorities in both cases. Meanwhile,

  • 10 of the 15 voters (6+4, or 67%) prefer Mangoes to Strawberries.

By pairing off all these preferences, we see the true preference order to be:

  1. Mangoes
  2. Strawberries
  3. Grapefruit…

The same as the Approval voting, and again, the exact reverse of what the Single Choice voting system produced.

While Ranked Choice provides pretty good subtlety and is less prone to manipulation than any of the other voting systems in the case of large anonymous public elections, it fails when compromise and soft preferences need to be considered.

 

For example, people rating the chances of success of 3 different plans.

Or 3 friends are choosing what toppings to order for a pizza. Two like pepperoni most and mushrooms close second. The third friend is vegetarian. Obviously, if they are truly friends, they will accommodate the needs of the vegetarian, but only approval and score voting can handle this scenario.

Score Voting

Voters give each option a Score. In our case we are using -5 to 5.

This means that in addition to providing information about their order of preference, voters are able to give information about the strength of the preference.

Scoring an option 1 and another option 2 means a weak preference, while scoring one option -5 and the other option 5 is a very strong preference. The scores are added and the option with the highest total wins.

Back to our example, let’s assume that, like many divisive options, people who like grapefruit love it, and people don’t like it REALLY don’t like it.

 

  • Six rank them like this: Grapefruit: 5/5, Mangoes 3/5, and Strawberries 2/5
  • Five rank them like this: Strawberries 5/5, Mangoes 4/5, and Grapefruit -3/5
  • Four rank them like this: Mangoes 5/5, Strawberries 3/5, and Grapefruit -4/5

When you add up all the points, you get:

  1. Mangos: Total= 58
  2. Strawberries: Total= 49
  3. Grapefruits: Total -1

Again, the same order as the other two methods and the exact reverse of what the Single Choice voting system produced. 

And again, if grapefruit had won, a majority of voters would walk away unhappy.

Because of Score Voting’s sensitivity to the strength of preferences, it is very sensitive to voters who are willing to give all the options except their favorite a low Score in order to get their top pick. For this reason, score voting is not typically used in large anonymous public votes.
However, in small groups with a high level of trust, who need to be able to make decisions with more subtlety and compromise, Score Voting is a good option.

That completes our tour of voting systems.

So you can see that many of the complaints we have with our political system may actually be a result of the actual voting systems we use, and would disappear totally if me mad a change.
Deciding on how our voting systems work in our democracies is one area where an upgrade is due, and one that could result in much better choices and much happier citizens.

So what does it look like to integrate all three of these systems?

That’s exactly what we have done with Forby.org.
Forby is a way for groups, large and small, to collect, develop, and prioritize the ideas of their members.

The main purpose of Forby is the crafting of ideas and proposals, and deciding what candidates are suited to any given position.

Members can then use our advanced voting system to come up with the best solution or candidate.

Here is the interface we are using.This interface allows us to run Approval, Ranked Choice, and Score voting simultaneously every time a voter votes. So a large community with little trust could rely on the rank, and small communities could rely on the score.
Quorum and ApprovalCommunity administrators set the quorum and approval percentages, and so the results of the vote shows whether the option passes the community’s approval percentage.
This is a results page. You can see the vote tally at the bottom.Here you can see your vote, the Rank, the Score, and the Approval.
You can like an idea but not think it is a high priority, so prioritization is separate.

As Forby grows and users get comfortable with a more detailed voting interface, coupled with finding that better voting system produce much better decisions, people may pressure governments to make the switch away from Single Choice voting.

If you are interested, sign up to use our software. It’s free to use and will allow you and any groups you are a part of, from family and friend circles to businesses, associations, boards, or coops, to make better decisions.