This simple graph illustrates something I’ve been thinking about lately. In one corner we have the the least fair situation that happens to be dead simple: despotism. We’d like our system of governance to be a little more equitable than that, so we walk over to the right and start running into complexity.

In some cases, we can move along the fairness axis without increasing complexity (e.g. recognizing an individual’s right to vote regardless of race or gender requires no augmentation of the electoral infrastructure). However, most changes increase both; The systems we put in place to improve representation tend to be more complex that living without them.

That being said, I recognize that electoral reform (specifically voting reform) will increase the complexity of our system. Fortunately, this is refinement in the right direction: a little more fairness at the cost of a little more complexity.

Refrigerators. We all know how to use them: we put things in, close the door and it keeps them cool for us. How many of us know how they work? Go ahead, draw me a diagram. When you’re done, see how it compares.

My point here is that it’s not really common knowledge. The mechanically curious might have a better idea, but it isn’t expected that the average person know the inner workings of our appliances, only how to use them.

Let’s say you had to build a refrigerator with what you know now. What’s the best you could do? Chances are the average person could throw together an ice box. Not bad, but certainly inferior to the product produced by professional engineers.

Knowing this, consider what would happen if engineers were restricted to only designing fridges that everyone could understand. We’d probably be stuck with something little better than the makeshift icebox. Doesn’t seem like a reasonable constraint, yeah? It doesn’t really matter how it works so long as it’s simple to use and the information is available to anyone with the curiosity and aptitude.

That being said, I feel that electoral reform has this unfair expectation that improved aggregate functions be sufficiently simple that the average person understands it in the first go. What’s more important is transparency of process and fair results.

• The ballot should be sufficiently simple for the voter
• The ballots should be easily tallied by hand
• The process of converting the tallies to winning candidates should be transparent and reproducible by those with the curiosity and aptitude.

So long as those constraints are met, we’re free to explore better systems without unnecessary handicaps.

There are two sides to voting systems: ballots and aggregate functions. Ballots describe individual voter preferences, whereas the aggregate functions convert batches of preferences into winning candidates. Having already discussed properties of the aggregate functions, let’s take a look at ballot types.

Checkmark ballots

	Mark one
Candidate A
Candidate B
Candidate C
Candidate D	X
Candidate E

If you’re from North America, this ballot type should look quite familiar. Voters express a preference for a single candidate. The ballot contains little information (in that no addition preferences are expressed), but it’s dead simple. It’s most frequently used in conjunction with plurality voting.

Checkmark ballot variants

	Mark any
Candidate A	X
Candidate B
Candidate C	X
Candidate D	X
Candidate E

Some variations on checkmark ballots exist, the most notable of which permits voters to select multiple candidates (see approval voting). While this increases the contained information, it does so at the cost of simplicity.

Preferential ballots

	Order
Candidate A	3
Candidate B	4
Candidate C	2
Candidate D	1
Candidate E	5

Instead of selecting candidates, preferential ballots ask voters to order the presented candidates from most to least favoured. More information is contained than vanilla checkmark ballots, but with the added burden of requiring voters to order all candidates. This type of ballot is used by instant-runoff voting.

Preferential ballot variants

	Order
Candidate A	2
Candidate B
Candidate C	1
Candidate D	1
Candidate E

Variants can address a number of the problems with preferential ballots. In the given example, note that the voter hasn’t ranked all candidates. Also note that the voter has ranked both Candidates C and D in first place. These two modifications increase the contained information while decreasing the complexity. Ballots that allow ties and unranked candidates require more aggregate functions, such as Ranked Pairs or the Schulze method.

Rating ballots

	Rank (-5 to +5)
Candidate A	0
Candidate B	-3
Candidate C	+5
Candidate D	+5
Candidate E	-5

In rating ballots, voters express preferences for each candidate independent of the others. Most notably, this ballot type includes magnitude of approval and, consequently, more information than any of the previously discussed types. While it’s certainly more complex than checkmark ballots, one could argue that it’s simpler than preferential ballots (doesn’t require strict ordering). This ballot type is most commonly associated with range voting.

Rating ballot variants

	Rank (0 to 3)
Candidate A	1
Candidate B
Candidate C	3
Candidate D	3
Candidate E

Variants modify the granularity of magnitude and the value assigned to unranked candidates. The given example is simpler than vanilla rating ballots, but contains the same information. The voter has expressed a strong preference for Candidates C and D, while at the same time expressing a weak preference for Candidate A.

Ballot conversions

We can map some ballot types onto others if our aggregate functions require it. For example, I very much like Ranked Pairs’ aggregate function. It’s reasonably simple and produces fair results that pass a large set of voting criteria. The down side is that it requires preferential ballots, when I prefer rating ballots. Let’s convert a rating ballot into a preferential ballot.

The end lesson here is that we can simplify our ballots without compromising too much on information density. I have the feeling that more people would be okay with rating each candidate than with explicitly specifying an order.

When I first got into electoral reform, I thought that I’d just need to explain it clearly enough. The more I try, the more I’m realizing that people just aren’t all that interested. Most understand what I’m describing and the majority agree that the proposed solutions are reasonable, but at the end of the day it just doesn’t sink in enough to spur action. I can appreciate why priorities are elsewhere; The issues of daily life seem far more pressing than something that happens once every few years.

Maybe I need to look at lessons learned in other fields. Marketing would probably have a fair bit to say about conveying the message in a stickier way. Electoral reform posters? I really don’t know, but I’m looking into it.

Update (September 5th)

I’ve converted these two posters into 30-second commercials.

When I was first investigating voting methods, I wanted to understand the various criteria by which they’re evaluated. Some are fairly straightforward

The majority criterion states that if there is a single candidate preferred by a majority of voters to all other candidates, then that candidate should win.

whereas others would be difficult to explain to anyone without a background in math.

Independence of Smith-dominated alternatives (ISDA) is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set, the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election.

Thinking about these helped move me away from “voting method X is awesome” towards “what criteria does this system satisfy?” There’s a whole list of them and it’s arguable as to which ones are relevant. To make the situation hairier, Arrow’s impossibility theorem says that no ranked preferences voting system can ever satisfy all criteria.

The next logical question to ask is which criterion is the most important. I ran across an old site where some guy talked about the evaluation of ranked-ballot voting methods. He ranks the criteria in order of importance to him in an attempt to determines which system best fits his concerns. Considering that everyone has different concerns, I’ve started to build a toy that will help that exploration.

You drag the tabs on the left in order of preference and the toy will tell you which voting systems satisfy your top criteria. The back-end logic was easy enough to build; Finding ways to concisely explain each criterion is turning out to be surprisingly difficult.

I’ve been working on a little project in my spare time to help vent the frustrations of disfranchisement. Under Canada’s current electoral system (first past the post), I can’t vote for my preferred candidate without wasting my vote. There are better systems out there, but they’re difficult to explain; Intuition and math don’t go hand in hand for most.

I hope this is a small step in the right direction: an interactive calculator that people can play with, modifying preferences and seeing what comes out of it. I’d think that most people’s intuition might agree with what Marquis de Condorcet knew back in 1785.

Curious about how this whole recent attempt at proportional representation started, I went looking through our history books and found, to my surprise, that we had it back in 1951. Dr. Ben Isitt’s The Ghost of Elections Past explains.

The 1950s was a period of social and political flux. The Liberals and Conservatives had formed a Coalition government a decade earlier, after the CCF won the most votes in a general election. […] The final act of co-operation between the Liberals and Conservatives was passage of the Provincial Elections Act Amendment Act, introducing the transferable vote in the spring 1951 legislative session. Both parties had endorsed the voting system at conventions in the 1940s. […] The Liberals expected to receive second preferences of Conservative voters, while Conservatives expected to be ranked second by Liberal voters.

In short, they figured they had the popular vote, but would stand to lose their seats due to vote splitting, one of the side effects of the first-past-the-post system. By switching to the instant-runoff voting system, they thought they would maintain their seats. What they didn’t seem to count on was that the Social Credit party had the popular vote and won out over the previous coalition in the subsequent election.

Social Credit – untested and untainted in the legislature – edged out the CCF, 19 seats to 18. The Liberals and Conservatives fell to six and four seats respectively. W.A.C. Bennett became premier with a minority Social Credit government. The next spring, he engineered his defeat in the legislature, won a majority mandate in a snap election, and promptly repealed the Provincial Elections Act changes. British Columbia returned to the old first-past-the-post voting system that prevails to this day.

Once the Social Credit party had the majority, they revoked the electoral reform. While it was put in place for self-serving reasons, IRV is a fairer electoral system (not perfect, but fairer). Bennett’s motivations aren’t detailed in the linked article and I don’t know if they’re documented anywhere, but the effect is the same.

Further reading

• History and use of the Single Transferable Vote in British Columbia
• History and use of instant-runoff voting in Canada

So we have this issue about riding sizes and how we make voter representative power proportional. The proposed solution in BC-STV was to amalgamate ridings and modify the number of representatives accordingly. On one hand, this balances the representatives with the population. On the other, smaller communities are unlikely to have anyone representing their issues. We can’t just split larger ridings up again and again, so what can we do?

One idea I’ve been batting around to keep the ridings the same size, but scale each single representatives’ voting power based on the their riding’s population at the time of the election. Sounds a little complicated at first, but let’s consider an example to clarify.

We have two adjacent ridings, one with 100 constituents and one with 50. Those in the smaller teal riding don’t want to be amalgamated for fear of losing their voice to two yellow-based representatives. Those in the yellow riding feel their voices are heard at half-volume as they have half as many representatives per person. Redrawing the line between yellow and teal doesn’t represent the reality of the geographic locales. So what do we do?

Instead of each representative having one vote in their legislature or what have you, the yellow representative would have 100 and the teal would have 50. This way the local issues of the teal riding are still voiced and the yellow constituents are represented proportionally.

I don’t know if there’s a name for this kind of system, but it could work fairly well at both the provincial and federal levels. Combined with a Condorcet method per riding, we could have a form of proportional representation that addresses the concerns with BC-STV.

Known issues

• If 51% of voters in each riding vote for party A and 49% vote for party B, we have a bit of an issue as the representatives are pretty far off from the popular vote. Voting reform helps mitigate this, but it’s still a concern.
• If a representative won their riding with 51% of the vote, they have the same voting power as a representative that won with 100% (assuming equal populations). I’m not fully convinced that this is bad just yet, but it’s worth looking at.
• The system doesn’t and can’t address how to get it in place over the current voting system. If the party in power stands to lose the most seats and also gets to set the bar for popular support, we’re somewhat boned.

Update

Turns out this notion is fairly similar to the population-weighted representation as put forth by James Madison in the Virginia Plan of 1787. It only differs in that Madison’s plan had two representatives for the yellow riding with one vote each, whereas mine has one representative with a voting power of 100.