what changes under proportional representation?

The short answers are nothing and everything. Or to be more precise, very little and a lot. It all depends on your perspective and on the system being considered.


Let’s start with election campaigns themselves. They won’t change dramatically but there will be subtle but important differences.

Central Campaign:

The central party campaign will still be important, as will the role of the party leader. They will continue to be the focus of media attention.

However parties will no longer be able to tell voters they need to vote tactically to prevent a horrible result. In fact such a tactic would likely backfire since, for example, a centrist party could form a coalition with either a leftist or rightist party. Voters worried about a rightist government would do better to elect more leftists than centrists.

Of course most people will just vote for whoever they believe best represents them. True centrists would be ambivalent to whether a coalition was left of centre or right.

That’s a small change but it is very important. Voters would be under no pressure to vote tactically. They could always vote sincerely.

Parties central campaigns would continue to be tactical as they present their stand on the issues they think will get them the most votes. Leftist parties will continue to campaign just to the left of the centrist party and rightist parties will campaign just to the right.

However it’s also possible that the left and right could each split into moderate and extreme groups, so that voters on all sides have choices. NDP too centrist for you? Vote for the Socialist Party instead. Conservatives too extreme, vote for the Progressive Conservatives. This will allow voters to be much more expressive in their voting choices.

Local Campaigns:

Outside of central campaign, there will be some minor changes in the local campaigns. The nature of these are partially dictated by the voting system. For example, under a pure list system or STV, parties will run regional candidates only. However no candidate can reasonably cover an entire region.

Instead candidates with regional visibility, such as popular incumbents and former media personalities, might devote most of their time to high profile events while less public figures will engage in ground campaigns targeting voters in their homes.

Of course, there will be fewer candidates in a region. While the Liberals were able to take all 25 Toronto seats in the 2015 federal election, they won’t do that under any proportional system. No party will run candidates that they know cannot win. So instead of 25 Liberal candidates, you may see anywhere from 12 to 20.

STV would probably see parties nominating the most candidates since they would need to have one or two more than they expect to be able to elect in a region. With STV requiring smaller regions, there will be more “also ran” candidates.

The converse is also true. STV may have smaller parties nominating fewer candidates than other systems. For example, when electing a single candidate would be a breakthrough for a party, they would need to nominate one per region. However if the system is MMP, the party may need to nominate candidates for each local seat to gain the ability to elect regional MPs.

Either way, from the point of view of a voter, the election campaign will look quite familiar. They’ll possibly see a local candidate from each party and will be bombarded with media coverage about other candidates from the same party.

Candidates will see a change in how they campaign. Well known candidates will concentrate more on big events while locally known candidates will focus more on their ground campaign.


This is were the big difference will be seen. The big difference of course being the bigger ballot. While under our current system, voters are faced with only candidate from each party, under any proportional system they will have a choice of many.

This doesn’t mean that voters have to know each candidate in order to make a choice and more that it does in the current system. What it does mean is that voters don’t have to vote for the party hack their favourite party dropped into their riding. If they like the party, they just need to find one of its candidates they feel is worth voting for.

Of course the choices vary by voting system. In an Open List system, you could just mark an X beside the name of your favourite candidate from a list from each party. In MMP you could face the same choice as our current system for the local candidate but the same choice as for Open List for the regional candidate. In either case tactical voting never enters into the decision process.

Under STV voters face a more complicate task. Being able to rank multiple candidates from each party is not an easy task even for a tuned-in voter. To make the task more manageable, parties resort to drone cards which provides a suggested ranking. In Australia’s senate races, almost every voter simply checks off a party’s rankings rather than risk spoiling their ballot.

Or voters may simply choose to not fully rank the candidate, listing only a few that they may have opinions on. This risks their ballot being “exhausted” (no more ranked candidates) before all the candidates in the region have been elected.

Either way the myth of the exquisitely informed voter ranking all the candidates in a region to get the most say in the election doesn’t really hold up. Practicalities get in the way.


Forming the government:

Again nothing changes but everything changes. After an election, the Prime Minister will still have the choice of trying to continue to govern or step down. Since most governments will be coalitions now, the Prime Minister’s decision won’t be so cut and dried as it currently is.

For example, when Paul Martin led the Liberals to defeat in 2006, they were facing a minority Conservative government. The Liberals + NDP + Bloc still controlled the most seats. Even if Paul Martin resigned as party leader over his handling of the election, a centre-left coalition could still have retained power.
Or the Liberals and Conservatives could have formed a Grand Coalition in the style of Germany’s Social Democrats and Christian Democrats.

Of course the same could have happened in Canada in 2006 even under our current system. However our current system is not kind to minority governments. Any of the coalition partners could trigger an election the moment they believe they can win a phony majority. That’s what Martin did in 2005, a decision that ended his political career.

That doesn’t happen in proportional representation. The voters wouldn’t have needed an inept Liberal campaign to punish the Liberals for triggering an unnecessary election, and Martin wouldn’t have had the lure of a phony majority to entice him to call one.

However 2006 did have an election and Martin’s party came in second. If he couldn’t or wouldn’t continue as Prime Minister, Harper would have been offered the chance to form one. Again this is exactly what happened.

However a Harper minority would need the support of another party or parties. It’s an open question whether the 2008 election would have happened under a proportional system. While Harper may still have asked for one, the Governor General could also have offered the Liberals a chance to form a government.

When one tries to form a coalition under PR, there are a lot of items up for discussion. There are specific issues of platform and also cabinet posts. Even the coalition leader, the Prime Minister, could be negotiated. This gives the coalition partners not just a say but also a stake in making the coalition work.

It also prevents parties from forgetting their election promises. Every point on a government’s agenda will discussed with their coalition partners and will be passed by representatives of the majority of voters. Parties cannot abandon their platforms without the voters abandoning them.

Being the government:

The aftermath of the 2011 election would have been much different. Harper’s Conservatives would not have had control of parliament. None of their omnibus bills would have seen the light of day since no party would have supported them. Instead of land mines buried in mountains of paper, Parliament would have demanded clear bills and proper debate.

Parliamentary committees would be fairly composed of members from all parties. Their work would include measures presented by those parties and would be properly debated on its merits.

Any coalition would have more than one party in the cabinet so pool of potential cabinet ministers is larger and the chance of getting a good one improve. The power of the Prime Minister is also diminished since cabinet decisions are just that – cabinet decisions. With the Prime Minister losing absolute control over cabinet, it becomes more democratic.

With more parties being privileged to government discussions, corruption is harder to cover up.

Because previous legislation had been passed by representatives of the majority of voters, the new government is also less likely to have to waste effort repealing ideologically driven legislation or overturning appointments to key posts.

In short, government is more likely work for the people. But if it doesn’t, the voters can turf the bums out in the next election knowing that their votes actually count.

Wrapping up:

The changes proportional representation brings aren’t big and obvious. Instead they are mostly subtle yet profound. The gridlock we see in the U.S. doesn’t happen in nations that elect parliaments using proportional representation.

Also gone is the spectre of demagogues getting the nuclear codes. Even Hitler never won anywhere near a majority of the seats in the Reichstags. He needed the help of compliant industrialists to circumvent their constitution in order to take control.

Once implemented however, proportional representation has proved remarkably resilient against campaigns to remove it. The voters like being in control and are loath to give that up.

Posted in Electoral Reform, History, Politics | Leave a comment

Left versus right

Been noticing something that really seems to distinguish the left from the right in politics these days. The left is all about doing the right things while the right is all about winning.

Some 20 years ago a Director where I used to work categorized it as the difference between being process oriented versus results oriented but it’s not really that. Processes can be changed as can goals. What doesn’t seem to change is that some people don’t care about the damage they do so long as they win while others don’t see “winning” as being that important. It’s the left that values getting the right results while the right values processes that lead to victory.

If you watched HBO’s docu-dramas on the 2000 U.S. presidential race and more recently the Clarence Thomas confirmation hearings where Anita Hill was dragged through the mud, you’ll understand what I mean. In both cases the Democrats wanted the truth to prevail no matter what it was while the Republicans wanted to make sure their guy won even he shouldn’t have.

In the former film, it was about finding out how the votes actually tallied, with the Republicans doing their best to stop a proper count. In the latter case it was wanting to get witnesses heard while the Republicans tried to discredit them and/or prevent them from testifying and/or using the news cycles to manipulate public perception.

Few children like to play with those who need to win at any cost. However when it comes to adult life where we don’t have to deal with them directly, our standards appear to be looser. Lots of people supported Rob Ford’s bullying and support Trump’s the same way.

Canada’s Liberals revealed the truth about their basic political orientation recently when they turned out in droves to support their Prime Minister’s bullying attempt to ram through the assisted dying bill.

My background is science and mathematics. They have changed the world more than all the conquerors and great leaders in history. They’ve been able to do this not by winning but by a dedication to getting the right results, no matter what they are.

Outside the ivory towers and research labs, it’s not always easy to figure out what the right results are. However we all should be aware that when something involves promoting hatred, bullying, lying, cheating or taking advantage of others then we shouldn’t be doing it.

Most of the big issues are not all that difficult to sort out if we all start with the simple premise that my group isn’t more important than your group. Unfortunately we get back to the original problem that some people just want to win. Their group will always be more important.

The way U.S. politics is going, we may soon have a megalomaniac with his finger on the nuclear trigger and the weight of the U.S. economy and military ready to ensure that “we’ll have so much winning, you’ll get bored with winning”. Half of America is cheering that premise.

That quite frankly scares the crap out of me.

Posted in Economics, Electoral Reform, History, Politics, Science and Mathematics, Sports | Leave a comment


There has been a lot written about “elbowgate”. I think the preponderance of it is absolute nonsense.

Most of what I have been seeing is criticism of Brosseau for complaining that she was elbowed in the chest. This is simply rubbish. No one outside of martial arts competitions should be expected to take an elbow in chest without comment.

Elbowing is even a penalty in that most gentlemanly of sports, professional hockey.

People often attempt to minimize it by saying it was just an accident. In this however they are decidedly incorrect.

Forgotten in most of the comments is that the whole reason Trudeau was in the area was to manhandle Conservative Whip Brown back to his seat. Grabbing his arm and forcibly dragging by itself constitutes assault.

One person even excuses the Prime Minister by saying the incident was over in a couple of seconds and that Trudeau let go when told to by Brown. However that too misses the point. Just because the perpetrator stopped the assault when told to, doesn’t mean the assault didn’t happen.

And that brings us back to why the assault on Brosseau wasn’t an accident.

If I am driving an automobile and hit someone, it may well be an accident. However if I was speeding, driving dangerously or driving while impaired then it is not.  As a reasonable licensed driver I am expected to know that doing any of those things can lead to collisions with people or objects.

Similarly when Trudeau stormed into the group of MPs, he should reasonably have known that he would almost certainly make contact with some members of that group. The fact that his intent while doing it was to commit an assault on Brown cements the case that the secondary assault on Brosseau cannot be treated as an accident. It was a direct result of Trudeau’s decision to assault Brown.

Unfortunately Trudeau’s defenders don’t stop there. They attack the very notion that Brosseau felt any pain. This also seems more like partisanship than an impartial review of the facts.

I’ve seen people compared it to being jostled in a subway. However that is obviously wrong. In a subway, your arms are usually down or above your head. When Trudeau grabbed Brown, his elbows were up – at chest level for the shorter Brosseau.

Blows to the chest can be very painful. A blow to the solar plexus can temporarily incapacitate the victim. Particularly in women, breasts can be very sensitive. Even hockey player’s pads protect the chest.

Even if she wasn’t struck in a sensitive area however, the victim of an assault doesn’t have to justify how much pain they might have felt.

The more rational parts of the Liberal caucus have admitted that what Trudeau did was wrong and he has apologized for it. Liberal partisans (and Conservative ones who have joined them in criticizing Brosseau) aren’t doing their party any favours by their attacks.

Nor are the supposed feminists who point out that Brosseau’s case bears little resemblance to that of an abused wife. No assault is justifiable. And one that occurs in your place of employment is worse than a random assault on the street because you have to be there on a daily basis. The fact that the person who committed the assault is also still there adds an extra dimension to the emotional pain.

Could it have been worse? Yes, of course. As assaults go, this was relatively minor. However it was committed by the Prime Minister. Canadians all have a right to expect him to set a better example. Instead his supporters are now using this incident to diminish expectations of what constitutes civil behaviour.

And that is what is at the core of elbowgate. A hot-headed Prime Minister acted rashly and his supporters are defending him. For many Canadians, this underscores the Liberal sense of entitlement that kept them from power the last ten years. Apparently they didn’t learn humility in their years in opposition.

Posted in History, Politics, Sports | Leave a comment

Journalists united against electoral reform

That is the title of an article written by Rick Salutin in today’s Toronto Star that does a loose expose of the way the media is against electoral reform. While he scores a number of good points about the failures of our current system, he also makes a number of mistakes that detract from the overall article.

One mistake he makes is in saying that first past the post only survives in Canada and the U.K.. Apparently he forgot about our neighbour to the South and India, along with a plethora of tiny former British colonies where the practice continues.

First past the post is actually the most popular winner-take-all voting system by a large margin, whether measured by nations using it or population governed by it. That’s because it actually is the least awful winner-take-all system.

And that is Salutin’s second, and larger, mistake. He says “Me, I’m good with any change.”

Any expert on electoral systems will tell you that there are many worse systems than first-past-the-post. And as I’ve pointed out in previous articles, choosing one of them actually makes future reform more difficult because once the system shows itself to be not worthwhile, it tars all electoral reform as a bad idea.

So for me, I’m decidedly NOT good with any change.

Of course Salutin’s article almost certainly was not written this way by accident or out of ignorance. Like other Toronto Star writers, he views elections as a tool to produce Liberal governments. First past the post has generally done that quite well. But a decade of Conservative governments with the Liberals slipping to third place led the Liberals to commit to electoral reform.

When they won a phony majority, they got stuck with bringing it in. And unlike previous “Liberal promises” this one committed to “making every vote count”, precise wording that leaves little wiggle room. To make matters worse, it specifically ruled out a referendum in its timetable.

So Salutin’s article is there to bolster the argument that the Liberals don’t have to actually “make every vote count”, so long as they end first past the post. To that end, he criticizes the NDP’s insistence on real reform and insists that any change is good.

In fact, the NDP’s position that only real reform should be considered is justifiable. It is Salutin’s position, that any change is better than none, that presents the real danger to electoral reform.

If we don’t get proportional representation this time out, public outrage might lead to electing a government that is really committed to it. If we get the atrocious ranked ballots (Alternative Vote or Instant Runoff) that the Liberals prefer, real reform is dead.

That’s the irony of Salutin’s headline. He’s doing as much disservice to real reform as the journalists he criticizes.

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Ontario introduces new election finance legislation

While the legislation has many positive aspects to it, it seems more like a grab bag of items that have been done before rather than a coherent policy aimed at putting politics in the hands of citizens. What’s lacking are answers to three fundamental questions:

1) what constitutes a political campaign, and
2) who should be allowed to give money to political campaigns, and
3) how much should they be allowed to give?

I believe that all campaigns attempting to influence the way people vote should be counted as political campaigns. The people who can contribute are those who live in Ontario. The amount they can give should be affordable by someone on social assistance.

So-called third party campaigns are blatantly political and attempt to get voters to vote for or against parties or candidates. They should be included in the contribution limits for individuals or subject to the same bans on donations as money or services directed to political parties.

And while each third-party campaign is subject to spending limits, what prevents moneyed interests from backing multiple campaigns? Moreover, why should individuals be allowed to contribute to both political parties and third party campaigns? Doesn’t that make a mockery of contribution limits?

Why should a third-party campaign representing hundreds of thousands of concerned citizens be subject to the same limit as one representing a few rich shareholders?

I am in favour of open debate between and during elections but I believe the rules should be based on the principle that all citizens have an equal say in these debates. The contribution limits should be based on what someone in the lowest echelons of our society can reasonably afford to give.

Whether I give directly to a political party or candidate, or to a group that conducts third party campaigns on my behalf (or some combination the three), the total amount I am allowed to contribute is what should be controlled.

The amount I give to a group that runs third-party campaigns, whether I give directly or through a group I am a member of, should be deducted from the amount I can give to political parties and candidates. This would give every citizen an equal voice. It would also prevent moneyed interests from outspending public interests in third party campaigns.

The limits I proposed however are below what political parties need to operate. We need some public money in the mix.

Both the federal government and our provincial one don’t like the idea of per-vote subsidies. Instead they want parties to raise more money from their support base. However this advantages those with enough money to contribute the maximum amounts and who are partisan enough to do so each year.

Unfortunately, with our winner-take-all electoral system, the per-vote subsidy means people who vote tactically find themselves supporting a party they only view as the lesser evil.

Why not instead have a check-off on the provincial tax return to send $1 to the party of your choice or to hold it to be allocated to a particular candidate in the next election? You could change your preference each year if you liked more than one party or if your preference changed. You wouldn’t be locked in like the per-vote subsidy.

Finally, let’s remove the reimbursements for political campaigns. Since the campaigns will be funded mainly by public money, there is no need to give it twice.

Rather than tinkering with a hodge-podge of tricks that benefit some parties more than others, let’s base our electoral finance legislation on putting the public in control.

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How to measure an electoral system

As I argued in my earlier post “The point of elections“, the quality of representation is the most important factor in discussing voting systems for a representative democracy. After all, the people elected are supposed to make decisions on behalf of the voters. If they don’t fairly represent the values and ideals of the people who elected them, what democratic legitimacy do their decisions really have?

Comparing how various voting systems stack up can therefore be largely (but not entirely) represented by how well they reflect the way people voted. There are some other factors that come into play, such as how much choice do they offer to voters and how well do they handle measures designed to counter systemic barriers, but generally these are secondary to the quality of representation.

There are three things that are useful in measuring the performance of a voting system. They are:

  1.  how well does the result match the way people voted (how proportional is it).
  2. how many people are represented by their first choice of candidate. This is clear and easy to understand as well as being easy to measure.
  3. how many people’s votes were actually effective in sending someone to Ottawa. This is great for highlighting the differences between systems.

1. index of disproportionality

The first measure involves math. Ideally the number of representatives a view gets should rise proportionally with the number of voters supporting that view. Picking people at random from the general voter list would achieve this quite well, but we don’t want our representatives to actually be just like us. We want them to be able to articulate the ideals and values that we hold. That’s something most of us can’t do very well, if we even know what they are. So instead we turn to elections.

This allows us to construct a way of measuring how well the election results reflect the way people voted. Ideally the number of representatives should rise directly with how many people voted a particular way. Any deviations from that straight line can be expressed as an “index of disproportionality” – a single number that tells you how crooked the line actually was.

For academics this is a very useful tool but there are various ways of deriving the number. And it doesn’t really give most people any measure they can relate to. It’s just a number.

2. first choice of representative

In our last election (and typical for most first past the post elections), half the voters got their “first choice” of representative. I put “first choice” in quotes because they only have one choice if they support a particular party and also because some people vote tactically to avoid what they consider to be a worse result.

Nonetheless, this is something people experience directly. Am I represented by someone I voted for or not? It doesn’t say anything about how satisfied you are with the result. You may have voted because you liked the candidate but hated the party or vice versa.  Short of mind-reading however, we can at least directly calculate how many people got the person they voted for.

In the recent federal election, 48.6% of voters got their first choice of representative. This is about half which means that about half the voters aren’t represented by anyone they voted for. This result is fairly typical for elections in Canada.

Preferential or ranked ballots (AV/IRV – Alternative Vote / Instant Runoff Voting) doesn’t change that figure. In fact, in the rare times when it changes the outcome of a race, the winner is the first choice of fewer voters.

Proportional systems work instead by giving more people their first choice of representative. Since a single representative won’t be everyone’s first choice, every proportional system uses some form of multimember districts.

A simple example of this is the semi-proportional Single Nontransferable Vote (SNTV). Each voter indicates the candidate they want to represent them in a multi-member district. If there are 2 representatives to be elected, the top 2 candidates (in terms of votes) win. If there are 3 to be elected, the top 3 candidates win, etc.. The more representatives to be elected, the more people get their first choice.

SNTV is quite good at giving people their first choice but the results aren’t as good in other measurements. The index of disproportionality is higher than in proportional systems because larger groups are actually often under-represented. Similarly the number of effective votes is lower than in proportional systems.

Single Transferable Vote (STV) elections also do quite well. With reasonable district magnitudes of 6 or 7 MPs (the practical limit) around 70% of voters get their first choice. This is the same number who would have under SNTV.

The reason the figure isn’t higher is that it takes about 15% of the votes to elect someone which also means that about 15% of the voters won’t elect anyone. The remaining voters, about 15% also, usually get their second choice. Unlike preferential/ranked ballots, their second choice is actually likely to be very similar to their first (probably a member of the same party).

Mixed Member Proportional (MMP) and list systems do much better. While some use closed (party) lists for part or all of the ballot, the ones that use open lists show that 90% of voters getting their first choice isn’t unusual.

Dealing with the simple open-list case first, you cast a single vote for your favourite candidate as in SNTV. In the case of a small-district SNTV system, this would give 70% of the voters their first choice of representative.

I confirmed this by calculating the number of voters for the party’s top candidates based on the regional seats they would have in the last federal election in the Toronto ridings if a 13/12 breakdown (about half) had been used for local versus regional seats.

Since the Liberals won all 25 seats, they would not have been entitled to any list seats. The Conservatives would have won 6, the NDP 5 and the Greens 1. Assuming that the local candidates were also list candidates and that their supporters voted for them in both roles, I took the top 12 Conservative candidates, the top 10 NDP and the top 2 Greens votes as a first approximation of how many list votes they would have received.

This again came up to about 70% of their total votes. The Liberals meanwhile got 100% of their first choices in the local races.

The convergence of these two lines of reasoning leads me to conclude that somewhere between 80% and 85% of voters would have elected their first choice of candidate had the last election been held using open-list MMP.

MMP and list systems do better than STV because they have simpler ballots and so are able to reasonably use much larger electoral regions than ranked systems like STV. The most complicated MMP ballot involves voting for a single local candidate (like in first past the post) and a second vote for either a regional candidate or a party. You only need to make two decisions whereas STV asks you to rank potentially large lists of candidates.

3. effective votes

The third measure, how many votes are actually effective, shows the real problem with first past the post. It takes one vote more than the second place finisher to win.In last year’s federal election only 29.9% of votes were effective. This again is typical, leading to the common complaint that votes don’t count. 7 times out of 10, they didn’t.

There are many ways to make more people’s votes count. AV/IRV does that by counting some people’s secondary preferences. While more people have an effective vote, fewer people get their first choice. In AV/IRV the share of effective votes is defined as 50%+1 in each riding.

Even the worst proportional system raises the tally of effective votes to 2 out 3. Reasonable implementation of STV can raise the figure to around 85% while MMP and list systems usually raise it to 95% of votes.

As I argued in section 2 above, the number of people getting their first choice of candidate in STV with a district magnitude of 6 or 7 is around 70%. An additional 15% get one of their secondary choices, raising the number of effective votes to about 85%.  As with AV/IRV, this is defined usually by the formula 1 + V / (N + 1) where V is the number of votes and N is the number of seats to elect.  Taking the number of votes to elect a candidate and multiplying that by the number of seats to fill, we get 86% to 88% effective votes but the last candidate often doesn’t meet the quota so the actual percent is a little lower.

With the simple MMP and List systems usually using larger district magnitudes, the number of effective votes increases. Taking Toronto as a single MMP or List region, the share of effective votes starts at around 87% (16+9 distribution) and goes up to almost 97% (25-seat list using the Hare quota)

No matter how you measure the representational performance of electoral systems, proportional representation wins hands down. There really is no room for discussion on that point.

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Innumeracy against electoral reform

Innumeracy is the math equivalent of illiteracy and it is a tool that is used by opponents of real electoral reform to muddy the waters. I recently had an online discussion with someone calling themselves ‘The Crucible” in which he tried to use this tactic. Unfortunately the site that hosted the discussion closed comments before I could rebut his misstatements.

I stated that in a typical winner-take-all election “the winner usually gets about 50% of the vote so the half the voters already have their first choice”.  He objected to this by claiming that only 39.5% of the candidates got more than 50% of the vote.

It should be obvious that the two statements are talking about different things.  My statement is saying that on average a winning candidate gets 50% of the vote – some get more and some get less.

The Crucible’s statement asserts that only 39.5% of the winning candidates actually got more than the average. This doesn’t refute my statement but merely says more winners got less than half the vote than more. The median winning share could be less than the average.

In fact, according to Elections Canada’s figures, the winning candidate actually got an average of 48.6% while 39.05% of candidates won with more that 50%. An additional 5% got 49% or more… While both our statements are accurate, the one about averages is more meaningful. The one that states how many candidates received more than 50% of the vote simply distracts from the argument that half the voters received their first choice of MP.

Perhaps more importantly, he then used his smaller numbers to argue that my calculations were wrong. This is not supported mathematically because the number of candidates above an arbitrary threshold is not important. The average number of voters who got their first choice is.

The reason why these numbers are important is that in a representative democracy, everyone should be represented by their first choice of candidate. Under first past the post, the number of voters who do that is only about 50% in typical elections.

Under Alternative Vote (AV, also called Instant Runoff or Preferential/Ranked ballot), the few times (less than 1 time in 20 usually) that the result might change, even fewer people get their first choice of candidate. That’s because AV only transfers votes from failed candidates. If your preferred candidate didn’t win, you are supposed to be happy with perhaps getting your second or third choice.

Proportional representation, on the other hand, works mostly by transferring excess votes from successful candidates. After your preferred candidate wins, any extra votes they received go toward electing like-minded candidates, so that most voters get not only their first choice but also possibly their second choice as well.

The fact that proportional representation uses multi-member districts is also critical. Multimember districts allows more than one group to elect a representative. More importantly, it allows more than one group to get their first choice of representative.

STV rarely uses district magnitudes (DM – number of people to be elected in a district) greater than 6 or 7. In the elections I’ve looked at, this give about 70% of the voters their first choice of candidate. For the other 30% of voters, you are expected to be happy with a secondary choice. While this 20% increase in the number of voters electing their first choice is significant, it can be improved upon.

The problem with STV is the relatively small DM. This is necessitated by the need to rank candidates, which requires some knowledge about candidates other than your first choice. Party affiliation usually plays the biggest role in this – a point The Crucible contests without offering evidence but that has been widely reported in studies.

In MMP implementations the seats are divided somewhere between 2/3 and equally between local and regional seats. The NDP’s proposal in the last federal election was for an open-list MMP system, where you vote for both a local and a regional candidate (although your regional vote could also be for the party’s ranking). Because you don’t need to know relative preferences but simply which local and which regional candidate you prefer, DMs can be much larger.

Because you have two votes, your first choice of either the local or regional candidate could be elected. Since the local candidates are elected using first past the post, half the time voters will elect their preferred local candidate. This effectively means that their regional votes won’t elect anyone because the local candidate they elected seat is deducted from their regional seat entitlement.

The voters who didn’t elect a local candidate basically elect the regional candidates. In practise all the votes actually go toward ranking the regional candidates for each party, but unless a party’s supporters in some local ridings have different preferences than in others, you can ignore the difference.

Within a party list, there is usually a clear gradient from the most popular to the least popular. We see this in STV lists by the first-choice preferences for the various candidates and in open lists by the number of votes each candidate gets.

Depending on the size of the list, the most popular candidate from a party could have anywhere from 20% to 100% (a list of one person) of the party’s support. Usually the winning candidates for a party get a clear majority of the votes for that party in that region. As per the STV example, in multi-member regions, you can see 70% of the voters get their first choice. In practise, because MMP regions usually have a much larger DM than STV regions, the percentage can be higher.

Combining the 50% of voters who elected a local candidate with the 70% or more voters (from the other 50% who didn’t elect a local candidate) who elected a regional candidate, we come up with 85% of voters electing their first choice of candidate.

I’m not going to claim this figure is carved in stone. It is a rough estimate based on reasonable assumptions and can vary quite a bit from one election or region to another. However the premise that MMP can give substantially more voters their first choice of representative is largely determined by how MMP operates.

We can confirm this by another rough calculation. With STV DMs limited to 6 or 7, it takes about 15% of the vote to elect a candidate. Smaller groups have a tough time getting their first choice. Even if they only run a single candidate, they need vote transfers from other groups but are at least as likely to see their votes transferred.

With MMP DMs can be (and frequently are) much higher. Even the more populous Atlantic provinces could have a province wide region electing all their candidate. Ontario, Quebec and some other provinces may prefer to split into smaller regions but they are still unlikely to be as small as STV regions.

With an MMP region electing perhaps 20 candidates, it takes only about 5% of the vote to gain representation. In fact because the local candidates are elected using first past the post, in a district electing perhaps 10 local candidates and 10 regional ones (hypothetical and not based on a particular model), while a candidate would need 5% of the vote in a 20-seat STV district, under fptp, they only need 1 vote more than the second place finisher.

In the last federal election, numerous candidates were elected with between 1/4 and 1/3 of the votes in their riding. This would translates into between 2.5% and 3.3% of the total vote.

These differences are why MMP can give more people their first choice than STV. By lowering the barrier to election, it can give more groups representation.

When you get into discussions with STV devotees, they often try to obscure the issues by introducing terms like party proportionality to suggest that there is an inherent virtue in ranking candidates instead of merely stating your first preferences. In practise their arguments fail these basic numerical tests.

While STV is a good electoral system, it’s not any better than any other simply because it allows you to do cross-party rankings. It comes with its own set of problems. There have been 10 significant studies of electoral reform for Canada since the turn of this century and they all have recommended MMP.

Rather than dispute the considered opinions of multiple groups of experts, STV advocates should get behind the notion that any form of PR is far better than any of the alternatives. Otherwise the representational limitations of STV compared with MMP could lead to shouting match that ends up giving us no reform.

STV advocates are probably slightly more numerate than the average voter. If they can’t wrap their heads around why their favourite system isn’t perfect, what effect do they think their misinformation will have on the more typical voter? Innumeracy and limited numeracy could sink electoral reform.

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