Tag Archives: electoral reform

Canada needs ranked, not proportional, voting

by Alexandre Normand Creative Commons

Image: Alexandre Normand, Creative Commons

February 11, 2017

Like many Canadians (even those of us who live abroad and may have dual citizenship) who had hoped that Prime Minister Justin Trudeau would follow through on his campaign promise to reform the voting system in Canada, I found myself deeply disappointed by his sudden announcement, that he had abandoned plans for reform and was sticking with the first-past-the-post system.

Canada is the only country in the OECD that still uses first-past-the-post in all elections. (England still uses it on its federal level, but uses different methods for voting on lower bodies.) It’s a dumb, dumb method. We’ve seen examples in Canadian provincial elections where a party has won the majority of the vote but lost the election – as in Québec several years ago. Under this idiotic system a party can gain five or 10% of public support and not have a single representative in parliament. This leaves a significant number of Canadians without anyone to voice their concerns. Trudeau was wrong, dead wrong, to abandon this promise in the way that he did.

He was not wrong, however, in saying that proportional representation was the wrong system for Canada. His comment to a woman who approached him in a mall – “How would you like to see Kelly Leitch with her own party?” – may seem flippant, but is absolutely on target. Proportional representation may seem like a good idea but there are too many examples of it creating problems rather than solutions.

The chance that a small right-wing party could gain enough votes to give it enough seats in the parliament to control the balance of power is a very real concern. If you want an example, just look at the state of Israel. Israel has been using proportional representation for years, and for years small right-wing religious parties have held enough seats to force whatever larger party they align with to enact often draconian anti-Palestinian legislation, even when the majority in the coalition disagrees.

The other problem with proportional representation is best seen in Italy. There are more parties in Italy than, as my mother used to say, Carter has little liver pills. This creates a parliament that looks more like a crazy quilt than a governing body. Under proportional representation the chance of an Italian party forming a majority government is almost impossible. While some people may say that is a desirable outcome, it’s also a way to guarantee governmental deadlock if you have too many parties, all clamoring for their agendas.

There is a better way to elect lawmakers and it is the ranked-choice system, which it appears Trudeau also prefers (and leaves me baffled why he would not move in this direction). It was also the system championed by third-party candidate Jill Stein in the United States. Under ranked-choice, also known as the “instant runoff” system, a voter is presented with the ballot on which he or she ranks those running for election in order of preference. When the ballots are counted the candidate with the fewest number of votes is dropped, and his or her votes are then distributed to the candidates picked as the second or third choice. This continues, until there are only two candidates for office left, with one candidate having the majority of votes and thus being declared the winner.

There are no perfect ways to run a democratic election. All systems have their flaws. For instance, one criticism of the ranked-choice method is that it could result in the election of a candidate who was only the first choice of a relatively small number of voters.

But ranked choice also offers several advantages in my view: it allows the possibility of a majority government while still offering smaller parties the chance to gain greater representation; it encourages voters to learn about candidates beyond their preferred one, reducing the “my family’s always voted this way and I’ve always voted this way” factor in elections;  it reduces the amount of negative advertising – after all if you’re trying to attract the second-place votes of Canadians who may not have chosen you first, that’s hard to do if you’ve trashed their first choice during the campaign; and it encourages coalition building.

On the one hand, I think Trudeau was wise not to move in the direction of proportional representation and I agree with him that, particularly in our current political environment, proportional representation could result in small parties on the left or the right having a disproportional influence on public policy.

However, the way he handled the decision to back away from his campaign promise was a serious mistake. Even if, as he says, the NDP was only willing to talk about proportional representation, he owed it to Canadians to do his best to sell them on the ranked-choice system if that is his preference, and to continue with reform.

Canadians need a new way to vote. The time of first-past-the-post is over, and the fact that Canada, which leads the world in so many other ways, is so behind in the way it conducts its elections, is a sad statement about its democracy.

‘Do you think Kellie Leitch should have her own party?’ Trudeau asks woman upset over electoral reform. CBC: http://www.cbc.ca/news/politics/electoral-reform-trudeau-leitch-1.3975354?cmp=rss

Ranked voting explained – CPG Grey: https://www.youtube.com/watch?v=3Y3jE3B8HsE

What is ranked-choice voting? – Jill Stein 2016: http://www.jill2016.com/ranked_choice_voting

Proportional voting explained, Youtube: https://www.youtube.com/watch?v=laUPeXZlPEg

Potential for odd outcomes in San Francisco mayoral election with ranked-choice voting system, says Stanford mathematician: http://news.stanford.edu/news/2011/november/devlin-ranked-voting-110711.html

Copyright Tom Regan 2017

Contact Tom Regan:  motnager@gmail.com




Tom Regan Tom Regan is a journalist in the Washington, D.C., area. He worked for the Canadian Broadcasting Corporation and with the National Film Board in Canada, and in the United States for the Christian Science Monitor, Boston Globe, and National Public Radio. A former executive director of the Online News Association in the U.S., he was a Nieman fellow at Harvard in 1991-92, and is a member of the advisory board of the Nieman Foundation for journalism at Harvard.

Return to Tom Regan’s page 



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Trump and Clinton prove America’s voting system is broken

Democracies everywhere are suffering. Voters protest. Citizens don’t vote. Support for the political extremes are increasing. One of the underlying causes, we argue, is majority voting as it is now practiced, and its influence on the media.

By Michel Balinski  an Rida Laraki 
May, 2016

Having outlasted all his opponents, Donald Trump is the presumptive nominee of the Republican Party. Hillary Clinton is closing in on locking up the Democratic nomination.

Clinton and Trump may have won primaries, but are they really representative of what the American people want? In fact, as we will show, it is John Kasich and Bernie Sanders who are first in the nation’s esteem. Trump and Clinton come last.

So how has it come to this? The media has played a big role, of course, but that Trump versus Clinton will almost surely be the choice this November is the result of the totally absurd method of election used in the primaries: majority voting.

This is a strong statement. But as mathematicians who have spent the last dozen years studying voting systems, we are going to show you why it’s justified and how this problem can be fixed.

With majority voting (MV), voters tick the name of one candidate, at most, and the numbers of ticks determine the winner and the order of finish. It’s a system that is used across the U.S. (and in many other nations) to elect presidents as well as senators, representatives and governors.

But it has often failed to elect the candidate preferred by the majority.

In 2000, for example, George W. Bush was elected president because of Ralph Nader’s candidacy. In the contested state of Florida, Bush had 2,912,790 votes, Al Gore 2,912,253 (a mere 537 fewer) and Nader 97,488. There is little doubt that the large majority of those who voted for Nader, and so preferred him to the others, much preferred Gore to Bush. Had they been able to express this preference, Gore would have been elected with 291 Electoral College votes to Bush’s 246. Similar dysfunctions have also occurred in France.

Imagine how different the U.S. and the world might be today if Gore had won.

A quick glance at the U.S. presidential primaries and caucuses held on or before March 1 shows that when Trump was the “winner,” he typically garnered some 40 percent of the votes. However, nothing in that result factors in the opinions of the 60 percent of voters who cast ballots for someone else.

As Trump is a particularly divisive candidate, it is safe to suppose that most – or at least many – of them strongly opposed him. The media, however, focused on the person who got the largest number of votes – which means Trump. On the Democratic side of the ledger, the media similarly poured its attention on Hillary Clinton, ignoring Bernie Sanders until widespread enthusiastic support forced a change.

An election is nothing but an invented device that measures the electorate’s support of the candidates, ranks them according to their support and declares the winner to be the first in the ranking.

The fact is that majority voting does this very badly.

With MV, voters cannot express their opinions on all candidates. Instead, each voter is limited to backing just one candidate, to the exclusion of all others in the running.

Bush defeated Gore because Nader voters were unable to weigh in on the other two. Moreover, as we argue further on, majority voting can go wrong even when there are just two candidates.

The point is that it is essential for voters to be able to express the nuances of their opinions.

Majority judgment (MJ) is a new method of election that we specifically designed to avoid the pitfalls of the traditional methods.

MJ asks voters to express their opinions much more accurately than simply voting for one candidate. The ballot offers a spectrum of choices and charges voters with a solemn task:

To be the President of the United States of America, having taken into account all relevant considerations, I judge that this candidate as president would be a: Great President | Good President | Average President | Poor President | Terrible President

To see exactly how MJ ranks the candidates, let’s look at specific numbers.

We were lucky to find on the web that the above question was actually posed in a March Pew Research Center poll of 1,787 registered voters of all political stripes. (It should be noted that neither the respondents nor the pollsters were aware that the answers could be the basis for a method of election.) The Pew poll also included the option of answering “Never Heard Of” which here is interpreted as worse than “Terrible” since it amounts to the voter saying the candidate doesn’t exist.

Screen Shot 2016-05-13 at 5.53.28 PM

Majority judgment of presidential candidates. Authors provided.

As is clear in the table, right, people’s opinions are much more detailed than can be expressed with majority voting. Note in particular the relatively high percentages of voters who believe Clinton and especially Trump would make terrible presidents (Pew reports that Trump’s “Terrible” score increased by 6 percent since January.)

Using majority judgment to calculate the ranked order of the candidates from these evaluations or grades is straightforward. Start from each end of the spectrum and add percentages until a majority of voters’ opinions are included.

Taking John Kasich as an example, 5 percent believe he is “Great,” 5+28=33 percent that he is “Good” or better, and 33+39=72 percent (a majority) that he is “Average” or better. Looked at from the other end, 9 percent “Never Heard” of him, 9+7=16 percent believe he is “Terrible” or worse, 16+13=29 percent that he is “Poor” or worse, and 29+39= 68 percent (a majority) that he is “Average” or worse.

Both calculations end on majorities for “Average,” so Kasich’s majority-grade is “Average President.” (Mathematically, the calculations from both directions for a given candidate will always reach majorities at the same grade.)

Similarly calculated, Sanders, Clinton and Cruz all have the same majority-grade, “Average President.” Trump’s is “Poor President,” ranking him last.

To determine the MJ ranking among the four who all are rated “Average,” two more calculations are necessary.

The first looks at the percentage of voters who rate a candidate more highly than his or her majority-grade, the second at the percentage who rate the candidate lower than his or her majority-grade. This delivers a number called the “gauge.” Think of it as a scale where in some cases the majority grade leans more heavily toward a higher ranking and in others more heavily toward a lower ranking.

In Kasich’s case, 5+28=33 percent evaluated him higher than “Average,” and 13+7+9=29 percent rated him below “Average.” Because the larger share is on the positive side, his gauge is +33 percent. For Sanders, 36 percent evaluated him above and 39 percent below his majority-grade. With the larger share on the negative side, his gauge is -39 percent.

Majority judgment ranking of presidential candidates. Authors provided

Majority judgment ranking of presidential candidates. Authors provided

A candidate is ranked above another when his or her majority-grade is better or, if both have the same majority-grade, according to their gauges (see below). This rule is the logical result of majorities deciding on candidates’ grades instead of the usual rule that ranks candidates by the numbers of votes they get.

When voters are able to express their evaluations of every candidate – the good and the bad – the results are turned upside-down from those with majority voting.

According to majority judgment, the front-runners in the collective opinion are actually Kasich and Sanders. Clinton and Trump are the trailers. From this perspective the dominant media gave far too much attention to the true trailers and far too little to the true leaders.

Tellingly, MJ also shows society’s relatively low esteem for politicians. All five candidates are evaluated as “Average” presidents or worse, and none as “Good” presidents or better.

But, you may object, how can majority voting on just two candidates go wrong? This seems to go against everything you learned since grade school where you raised your hand for or against a classroom choice.

The reason MV can go wrong even with only two candidates is because it does not obtain sufficient information about a voter’s intensity of support.

Take, as an example, the choice between Clinton and Trump, whose evaluations in the Pew poll are given in the first table above.

Lining up their grades from highest to lowest, every one of Clinton’s is either above or the same as Trump’s. Eleven percent, for example, believe Clinton would make a “Great” president to 10 percent for Trump. Trump’s percentages lead Clinton’s only for the Terrible’s and Never Heard Of’s. Given these opinions, in other words, it’s clear that any decent voting method must rank Clinton above Trump.

However, majority voting could fail to do so.

To see why, suppose the “ballots” of the Pew poll were in a pile. Each could be looked at separately. Some would rate Clinton “Average” and Trump “Poor,” some would rate her “Good” and him “Great,” others would assign them any of the 36 possible couples of grades. We can, therefore, find the percentage of occurrence of every couple of grades assigned to Trump and Clinton.

We do not have access to the Pew poll “ballots.” However, one could come up with many different scenarios where the individual ballot percentages are in exact agreement with the overall grades each received in the first table.

Among the various scenarios possible, we have chosen one that could, in theory, be the true one. Indeed, you can check for yourself that it does assign the candidates the grades each received: reading from left to right, Clinton, for example, had 10+12=22 percent “Good,” 16+4=20 percent “Average,” and so on; and the same holds for Trump.

So what does this hypothetical distribution of the ballots concerning the two tell us?

The first column on the left says 10 percent of the voters rated Clinton “Good” and Trump “Great.” In a majority vote they would go for Trump. And moving to the tenth column, 4 percent rated Clinton “Poor” and Trump “Terrible.” In a majority vote this group would opt for Clinton. And so on.

A hypothetical head-to-head matchup. Authors provided

A hypothetical head-to-head matchup. Authors provided

If you add up the votes in each of these 11 columns, Trump receives the votes of the people whose opinions are reflected in four columns: 10+16+12+15=53 percent; Clinton is backed by the voters with the opinions of columns with 33 percent support; and 14 percent are undecided. Even if the undecided all voted for Clinton, Trump would carry the day.

This shows that majority voting can give a very wrong result: a triumphant victory for Trump when Clinton’s grades are consistently above his!

Voting has been the subject of intense mathematical research since 1950, when the economist Kenneth Arrow published his famous “impossibility theorem,” one of the two major contributions for which he was awarded the 1972 Nobel Prize.

Marquis de Condorcet (1743-1794) was a French philosopher and mathematician.

This theorem showed that if voters have to rank candidates – to say, in other words, who comes first, second and so forth – there will inevitably be one of two major potential failures. Either there may be no clear winner at all, the so-called “Condorcet paradox” occurs, or what has come to be called the “Arrow paradox” may occur.

The Arrow paradox is familiar to Americans because of what happened in the 2000 election. Bush beat Gore because Nader was in the running. Had Nader not run, Gore would have won. Surely, it is absurd for the choice between two candidates to depend on whether or not some minor candidate is on the ballot!

Majority judgment resolves the conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow paradox can occur. It does so because voters are asked for more accurate information, to evaluate candidates rather than to rank them.

MJ’s rules, based on the majority principle, meet the basic democratic goals of voting systems. With it:

  • Voters are able to express themselves more fully, so the results depend on much more information than a single vote.
  • The process of voting has proven to be natural, easy and quick: we all know about grading from school (as the Pew poll implicitly realized).
  • Candidates with similar political profiles can run without impinging on each other’s chances: a voter can give high (or low) evaluations to all.
  • The candidate who is evaluated best by the majority wins.
  • MJ is the most difficult system to manipulate: blocs of voters who exaggerate the grades they give beyond their true opinions can only have a limited influence on the results.
  • By asking more of voters, by showing more respect for their opinions, participation is encouraged. Even a voter who evaluates all candidates identically (e.g., all are “Terrible”) has an effect on the outcome.
  • Final grades – majority-grades – enable candidates and the public to understand where each stands in the eyes of the electorate.
  • If the majority decides that no candidate is judged an “Average President” or better, the results of the election may be rescinded, and a new slate of candidates demanded.
  • It is a practical method that has been tested in elections and used many times (for judging prize-winners, wines, job applicants, etc.). It has also been formally proposed as a way to reform the French presidential election system.

It should come as no surprise that in answer to a recent Pew poll’s question “Do you think the primaries have been a good way of determining who the best qualified nominees are or not?” only 35 percent of respondents said yes.

Democracies everywhere are suffering. Voters protest. Citizens don’t vote. Support for the political extremes are increasing. One of the underlying causes, we argue, is majority voting as it is now practiced, and its influence on the media.

Misled by the results of primaries and polls, the media concentrates its attention on candidates who seem to be the leaders, but who are often far from being deemed acceptable by a majority of the electorate. Majority judgment would correct these failings.

The ConversationCreative Commons

Michel Balinski is an applied mathematician and mathematical economist, “Directeur de recherche de classe exceptionnelle” (emeritus) of the C.N.R.S. , École Polytechnique – Université Paris Saclay.  Rida Laraki is Directeur de recherche CNRS au LAMSADE, Professeur à l’École polytechnique, Université Paris Dauphine – PSL.  This article was originally published on The Conversation. Read the original article.


You may also be interested in these democracy-related stories:

Canada’s strategic, desperate, election: Anybody But Conservative, by Deborah Jones, Free Range column

The shambles of Canada’s democracy, and paralysis in the face of existential economic, environmental and civil threats to the country I call home, drove me from being a lifelong, carefully non-participatory journalist observer of politics, into activism during this federal election.

Fox News Facebook page

The art of manipulating campaign coverage, by Tom Regan, Summoning Orenda column

Who is manipulating whom in media coverage of United States politics? American media manipulates the way they tell stories in order to increase eyeballs and produce a narrative that suits their tastes. But politicians then manipulate the media into creating those narratives and building on them, despite what is actually going on in the campaign.

Ideal democracy hears both whispers and shouts. By John Wright

To have a healthy democracy, it is not enough to hold regular elections, or for every person to get one – and only one – vote. At the heart of democracy is the idea that by voting for a particular party, the people confer upon that party legitimate authority to govern. But if a vote is to justify a ruler’s claim to authority, a number of conditions need to be met.


Facts and Opinions is a boutique journal of reporting and analysis in words and images, without borders. Independent, non-partisan and employee-owned, F&O is funded by our readers. It is ad-free and spam-free, and does not solicit donations from partisan organizations. To continue we require a minimum payment of .27 for one story, or a sustaining donation. Details here; donate below. Thanks for your interest and support.

F&O’s CONTENTS page is updated each Saturday. Sign up for emailed announcements of new work on our free FRONTLINES blog; find evidence-based reporting in Reports; commentary, analysis and creative non-fiction in OPINION-FEATURES; and image galleries in PHOTO-ESSAYS. If you value journalism please support F&O, and tell others about us.

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Ideal democracy hears both whispers and shouts

By John Wright,  University of Newcastle
December, 2014

The hustings (Charles James Fox), by James Gillray published 1796. National Portrait Gallery, London, via Wikipedia Commons.

The hustings (Charles James Fox), by James Gillray published 1796. National Portrait Gallery, London, via Wikipedia Commons.

To have a healthy democracy, it is not enough to hold regular elections, or for every person to get one – and only one – vote. At the heart of democracy is the idea that by voting for a particular party, the people confer upon that party legitimate authority to govern.

But if a vote is to justify a ruler’s claim to authority, a number of conditions need to be met.

What is a person doing when they tick a box on an election paper? Most directly, they are expressing a preference to be governed by that party.

They will usually have reasons for choosing that party over another. Perhaps they believe interest rates will be lower under that party, or the economy will be better-off. Or, perhaps they think that party will make their country a fairer place to live. Overall, they may think that party is more likely to make Australia the type of place the voter thinks it ought to be.

Now it may be a matter of debate whether or not the voter’s reasons are well-founded. Consider the belief that “interest rates will remain lower under Party A”. Although a voter might sincerely believe this to be true, they may or may not have good reasons for the belief.

Unless the voter is an economist, they will rely on the expressed views of others for their opinion. And it seems reasonable to suppose the voter will be influenced by voices that have gained prominence in public discussion.

We now come to a central point. Public discussion may be more balanced and comprehensive, or less balanced and comprehensive. Some points of view might be given a thorough airing, while others are barely heard at all.

Now suppose, hypothetically, public discussion was strongly skewed in one direction. A voter – let’s call him Smith – decides to vote in a certain way as a result of being exposed to this one-sided discussion. More specifically, he decides to vote for Party A because the discussion to which he has been exposed tells him they will keep interest rates lower.

Only after the election does Smith learn there was another side to the issue. He might, for example, discover that, actually, interest rates were no more likely to remain low under Party A. He might then declare, “If I had learnt about this other side before the election, I would have voted the other way.”

Under these circumstances, would we say that Smith’s vote had helped confer legitimate or justified authority on the elected government? I think we are inclined to say that if it did so, then it did only to a reduced or qualified extent.

And if many people would have voted the other way had they been exposed to a more comprehensive or balanced public discussion – in particular if the outcome of the election would have been different – then we might say the government’s claim to have justified authority would be at least reduced. It might even be claimed that, in the relevant sense, the government does not have justified authority.

This seems to suggest that, in a democracy, if an elected government is to have a strong or full claim to justified authority, public discussion before the election must be “sufficiently” comprehensive and balanced. The more comprehensive and balanced, the stronger the elected government’s claim to justified authority.

This raises the question: “What ensures that public discussion will be comprehensive and balanced?” A brief answer is: it is more likely to be comprehensive and balanced if all wishing to have a say in the public discussion have a more or less equal power to be heard.

In a society strongly divided into “haves” and “have-nots”, that power is not distributed equally. The wealthy will, in a variety of ways, be better able to get their point of view heard: they can afford advertising, publicists or lobbyists, they can help to finance “think-tanks” and, in a small number of cases, they can own media outlets.

Writing about the (rather worse) situation in the US, political scientist Lawrence Jacobs wrote, “Citizens with lower or moderate incomes speak with a whisper that is lost on the ears of inattentive government officials, while the advantaged roar with a clarity and consistency that policy-makers readily hear and routinely follow.”

A society that is split between rich and poor is a society split between those with the power to be heard in public discussion and those that lack such power. A society with a more equal distribution of wealth is one more likely to produce balanced and comprehensive public discussion and so more likely to confer fully justified authority on those elected on the basis of that discussion. Equality is good for the health of democracy.

Creative Commons

The Conversation

John Wright is an Australian academic. He does not work for, consult to, own shares in or receive funding from any company or organization that would benefit from this article, and has no relevant affiliations. This article was originally published on The Conversation. Read the original article.


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