Voting for pizza: electoral reform illustrated

So electoral reform is on my mind again – no, not for that reason, but because the next federal election is coming up. Last year I wrote a post for Canadian Atheist about electoral reform, and I was shocked and horrified to discover how little most Canadians know about the issue. My goal this year is to shine a little more light on it.

As I put it at the time, it felt like I had made a post about how global warming specifically impacts Canada… only to be greeted with confusion and doubt about whether global warming is actually a thing. That should not be possible in 2014, and certainly not on a blog focused on atheism and freethought. We’re past that stage. Everyone by now should know that global warming is real, and a real problem.

Well, that should also be the case with electoral reform. Every Canadian, in 2014, should have been at least marginally aware that our First Past the Post electoral system – used top-to-bottom, from the municipal level up to the federal – is archaic and broken. We had more than enough evidence by that point. We literally have one of the worst electoral systems in the developed world. Literally, according to the metric of whether the makeup of our parliament actually reflects voters’ preference. (See the Canadian Atheist post for details.)

Electoral reform may be coming – the only major federal party that doesn’t support it is the Conservative Party, natch – but we are actually at a dangerous and crucial point. The problem is that the Liberal Party is flip-flopping between a proportional system… and “Alternative Vote” (also known as “Instant Runoff Voting”). (All other parties, except the Conservatives, explicitly support proportional representation.)

An AV/IRV system would be no real improvement. It is “better” than FPTP, but only in the sense that eating a frosted turd is better than eating one without frosting.

Allow me to demonstrate.

I learned my lesson, after that Canadian Atheist article, about assuming that the problems with the Canadian electoral system are common knowledge. I can no longer simply assume that everyone already understands why proportional representation is the only fair representation. I need to illustrate the claim. Thanks to a dispute with my sister and her man-candy about what to order for dinner one evening, I came up with a way.

Imagine a group of 12 people want to order pizza. The size of the pizzas and the appetites of the people means that 1 pizza will feed 3 people, so 4 pizzas are necessary.

The only thing left to decide is the toppings. But of course, everyone has different preferences.

It breaks down like this:

  • A, B, C, D, and E want a meat lover’s pizza.
  • F wants a pepperoni pizza, but will settle for meat lover’s.
  • G, H, and I want a pepperoni pizza.
  • J wants a vegetarian pizza.
  • K wants a vegetarian pizza, but will settle for pepperoni.
  • L wants a plain cheese pizza, but will settle for vegetarian, or pepperoni in the worst case.

They all agree to vote on what pizzas to get… but let’s see what happens when we use different electoral systems.

Let’s start with the current system used across Canada: First Past the Post. This system is very simple. You just tally up what everyone wants, and whichever option gets the most votes, wins. Here’s how the votes break down:

Person Meat lover’s Pepperoni Vegetarian Cheese
A
B
C
D
E
F
G
H
I
J
K
L
Totals 5 (42%) 4 (33%) 2 (17%) 1 (8%)

The winner is “meat lover’s pizza”. Therefore, the group orders 4 meat lover’s pizzas.

Is that fair? After all, the “meat lover’s” option didn’t even get half the votes. 58% of the group isn’t getting their first choice. A full 50% isn’t getting any option they like.

Can’t we do better than this?

Let’s try AV/IRV.

Alternative Vote – also called Instant Runoff Voting – is another non-proportional system similar to First Past the Post, except it uses ranked ballots and considers other choices beyond the first pick. An AV/IRV count happens in multiple rounds. In the first round, everyone’s first choice is counted. If any option has a true majority – at least 50%+1 – they are the winner. But if no option has a true majority, the option with the lowest count is eliminated, and all the ballots that ranked that option are recounted – ignoring the first choice pick, so the second choices are counted. Once again, if any option has a true majority, it wins. If not, the lowest-tallied option is eliminated again, and the process is repeated until one option finally has a true majority.

Here’s how it breaks down in this case. The first count would go exactly as in the previous example. The option with the lowest tally is “cheese pizza”, so it gets eliminated, and all ballots it got – just one, L’s – are recounted, ignoring the eliminated option:

Person First round

Second round
ML P V C ML P V
A
B
C
D
E
F
G
H
I
J
K
L
Totals First round

Second round
5 (42%) 4 (33%) 2 (17%) 1 (8%) 5 (42%) 4 (33%) 3 (25%)

Still no majority, so the option with the lowest tally – “vegetarian pizza” – is eliminated, and the ballots that selected it are recounted (ignoring the already eliminated options).

Those ballots are J, K, and L’s ballots. All options on J’s ballot have been eliminated, so J is effectively no longer relevant to the election. The new count gives:

Person First round

Second round

Third round
ML P V C ML P V ML P
A
B
C
D
E
F
G
H
I
J
K
L
Totals First round

Second round

Third round
5 (42%) 4 (33%) 2 (17%) 1 (8%) 5 (42%) 4 (33%) 3 (25%) 5 (45%) 6 (55%)

“Pepperoni” has more than 50% of the vote, so it wins. Therefore, the group orders 4 pepperoni pizzas.

Is that fair? It is true that the majority of the group will accept a pepperoni pizza. However, only 33% of the group wanted it as their first choice. And even though meat lover’s is the most desired first choice, no one gets it.

Can’t we do better than this?

Enter proportional voting. There are various mechanisms to achieve it, which I won’t describe here because right now I’m just proving that the concept of proportional representation is the only fair one. The details of how to achieve proportionality are for another post.

The concept is simple: you just count all the votes, and tally up the options. But then, rather than simply picking the most popular one and forcing it on every one, you look at the proportion of votes each option got and try to distribute the winners to best reflect that.

The vote results are exactly as they are in the first example (the FPTP) example, except now we look at the proportions:

  • Meat lover’s: 42%
  • Pepperoni: 33%
  • Vegetarian: 17%
  • Cheese: 8%

There are 12 voters, but only 4 pizzas will be ordered, so the results are quantized at 25%:

  • Meat lover’s: 42% is closer to 50% than 25%
  • Pepperoni: 33% is closer to 25% than 50%
  • Vegetarian: 17% is closer to 25% than 0%
  • Cheese: 8% is closer to 0% than 25%

Which gives:

  • Meat lover’s: 50%
  • Pepperoni: 25%
  • Vegetarian: 25%
  • Cheese: 0%

Or in other words: 2 meat lover’s pizzas, 1 pepperoni, and 1 vegetarian.

Note that not everyone gets the first pick (and L is lucky to even get his second pick). Proportional representation isn’t magical – it can’t give everyone everything they want. It is simply mathematically impossible, for example, to promise to allocate 308 seats in a way that satisfies every single person in a voting population of 25 million. But it is far better than either FPTP or AV/IRV at making sure that most people get what they want – or rather that the results best represent the desires of the voters. And shouldn’t that be the point of a fair voting system?

Now, you might object that I’ve cheated a little by having one vote for 4 pizzas. Both FPTP and AV/IRV select single winners, while PR can select multiple winners. Doesn’t that make this whole comparison moot?

No, actually. In fact, you’ve just found another problem with FPTP and AV/IRV, with respect to the Canadian system. Let me explain.

What I did was use the pizza order as an analogy to parliamentary power… and there’s only a single parliament made up of multiple members, just as there is only a single order made up of multiple pizzas. As you saw, with PR it… just worked. Nothing more required. With no effort, PR gave us a fair and representative government-slash-pizza-order made up of multiple members-slash-pizzas. Neither FPTP nor AV/IRV worked out of the box.

So how would we change things to make FPTP and/or AV/IRV work better for this kind of case? Well, that’s easy: We say each pizza is a “riding” or “district”, and split the voters up into one of the 4 ridings – one for each pizza. Each riding has only a single winner, selected only by the 3 members of that riding using FPTP or AV/IRV. The four winners of the four ridings combine to form the total pizza order. If that sounds familiar, that’s actually the current electoral system in Canada – using FPTP, of course, but you could just as easily swap it for AV/IRV.

Ah, but here’s the million-dollar question: How do you divide up the 12 people into the 4 ridings?

Think it doesn’t really matter? Well dig this. Suppose I was the guy organizing the grouping, and I really wanted lots of meat lover’s pizzas to be ordered (maybe hoping for leftovers, or something), and really didn’t want to see a single pepperoni pizza. I could easily organize the ridings like this:

Riding 1
A (meat lover’s), B (meat lover’s), G (pepperoni)
Riding 2
C (meat lover’s), D (meat lover’s), H (pepperoni)
Riding 3
E (meat lover’s), F (pepperoni, meat lover’s), J (vegetarian)
Riding 4
I (pepperoni), K (vegetarian), L (cheese, vegetarian, pepperoni)

The results (assuming ties are resolved using second choices) are: 3 meat lover’s and 1 vegetarian.

What if, instead, I wanted lots of pepperoni, and no meat lover’s? I could do this:

Riding 1
A (meat lover’s), B (meat lover’s), C (meat lover’s)
Riding 2
D (meat lover’s), G (pepperoni), K (vegetarian, pepperoni)
Riding 3
E (meat lover’s), H (pepperoni), L (cheese, vegetarian, pepperoni)
Riding 4
F (pepperoni, meat lover’s), I (pepperoni), J (vegetarian)

It’s mathematically impossible to prevent meat lover’s from winning any riding (there are 5 people with meat lover’s as their first choice, and 4 ridings… at least one riding will have 2, which is an automatic victory when each riding has 3 people). Nevertheless look what I accomplished: 3 pepperoni and 1 meat lover’s.

Note that the preferences of the voters didn’t change. All that changed is how I drew the riding boundaries. This is gerrymandering. It may seem silly to do this for a pizza order, but consider it in the context of parties and government. By carefully selecting the riding boundaries, the pepperoni party can get 3, 1 (in the fair, proportional case), or 0 seats. If the pepperoni party is in power, it can give itself an even greater advantage… if the meat lover’s party is in power it can virtually eliminate its greatest threat. Remember, electoral district boundaries are selected by the party in power. With gerrymandering, they can solidify and even expand their power in the next election, regardless of voter preferences.

And here’s the punchline. Suppose a diehard FPTP or AV/IRV supporter insisted that while gerrymandering is a potential problem, it can be avoided simply by arranging the ridings so that the final results are actually fair and representative. Just smile sweetly at them and ask, “okay, how would you do that?”, then watch the embarrassment spread slowly across their face when they realize the answer is: proportional representation.

FPTP is not a fair system. AV/IRV is a slight improvement, but still not fair. The only fair way to collect the preferences of the entire electorate and use them to determine the makeup of the elected body is proportional representation.

It is time – long past time – for Canada to abandon the archaic and undemocratic First Past the Post electoral system, at all levels of government (but particularly federal and provincial).

Switching to an Alternative Vote/Instant Runoff Voting system is not an option – it is effectively the same undemocratic system with only a very slight improvement. FPTP allows an absolute minority to hold tyranny over all (42% in the pizza example, but more like 30–35% at the federal level in Canada – more like 18–20% if you consider the turnout). AV/IRV at least ensure that the tyranny is done by an absolute majority… but it’s still tyranny of the entire population by a subgroup. Proportional representation ensures, insofar as it is practically possible, that the entire population has a say in how they are governed.

Accept no substitutes. Demand from your representatives that Canada moves to a fair and democratic electoral system: a proportional system.

For more information, check out Fair Vote Canada.

(Edit: after writing this post, but before publishing, I was alerted to the existence of “First Past the Pizza”. Coincidentally, one of the titles I considered for this post was also “First Past the Pizza”. And, of course, the meat lover’s option won in both cases.)

CC BY-SA 4.0
Voting for pizza: electoral reform illustrated by Indi in the Wired is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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