Thursday, March 06, 2014

Building a seat model for New Brunswick

The idea behind a seat model is to try to convert the popular vote estimates from an opinion poll into a seat count as the latter is far more relevant to our politics.

The fact that Richard Hatfield lost the popular vote in 1974, did not prevent him from being premier of a majority government for four years before winning the popular vote in 1978 and 1982. The fact that 40% of New Brunswickers voted for non-Liberal candidates in 1987, did not get any of them elected. More recently, Shawn Graham also won a majority government while losing the popular vote in 2006.

To summarize: the popular vote doesn't tell the whole story in our system of government. It is the seats that count.

The Method

There are two general approaches that one can take in a seat model. Uniform swing or proportional swing.

Uniform swing has been used for years in Britain and Australia.

It means that all parties take the same arithemetic benefit or loss from their change of support throughout the jurisdiction. So if the Labour vote is down by 10 percentage points from 40 to 30, it drops by 10 percentage points in every riding. In riding X, their support drops from 50% to 40% (which means they've lost 20% of their base votes), in riding Y it drops from 15% to 5% (which means they've lost 67% of their base votes).

The alternative is proportional swing. This is what is generally used by election projectionists in North America, including the site which has projected a lot of Canadian elections from polls. Calgary Grit and FiveThirtyEight use seat models which are built on a base of proportional swing, with many other fancy features.

It means that parties move in support relative to their base. So if the Labour vote is down by 10 percentage points from 40 to 30, it drops by 25% in every riding, meaning they take a relatively bigger hit in ridings were they had more votes to lose. In riding X, their support drops from 50% to 37.5% (25% of 50% is 12.5 percentage points), in riding Y it drops from 15% to 11.25% (25% of 15% is 3.75 percentage points).

The teaser seat modelling I have done on Twitter has been based on a proportional swing method.

I have spent the past several weeks improving and testing the model in anticipation for the main event in September.

One of the things I tested was each of the past 5 elections' popular vote versus the actual results in seats.

Interestingly, I found that proprtional swing does a better job producing the overall provincewide seat total. However, it does this while making many errors at the local seat level which tend to cancel each other out. While the uniform swing doesn't do quite as will with the final overall result, it does do a better job at the local seat level (its errors tend to be in one direction rather than both, so its overall numbers are worse).

I played around with a number of "half-way" alternatives. The most simple of these, taking the result under uniform swing and under proportional swing and simply averaging them proved to work the best. On average it tied the uniform swing for accuracy at the local level, and proportional swing for accuracy at the provincial level. I will be using this hybrid model going forward.

This model uses results of the 1995-2010 general elections as a base. I have transposed the 1995-2003 ridings and the 2006-2010 ridings onto the new boundaries to be used for the 2014 election. The 1995-2003 are weighted half as much as the two more recent 2006 and 2010 elections to create an "average" election result from which the model builds its projection based on change in the popular vote from that hypothetical election to what the opinion polls are saying. For the Greens and PANB, their 2010 results are used as a base as that is the only election they have contested. Votes for defunct parties and independents are ignored by the model.

This model is not as fancy as the models used by Calgary Grit and FiveThirtyEight, which model thousands of iterations based on the margins of error, etc and generate a percentage liklihood of each parties' chance of winning a particular riding. I do run about a dozen scenarios through the model pushing each party to the upper and lower range of the margin of error to generate seat ranges.

Adjustments: A Hand Up for the Leader

Another measure that I have incorporated into the model is a "leader bounce".

I've looked at the result of the leader in his or her riding in those elections he or she contested, and that of his or her party in that riding in the elections immediately before and after his or her leadership tenure. This allows one to assume how a generic candidate of the leader's party might have done in that riding so that it can be compared to the leader's result.

For instance, Robert Higgins led the Liberal Party in the 1974 election. He ran in the riding of Saint John Park. He received 14.6 percentage points more of the popular vote in his riding than the Liberal Party did provincewide. We cannot look at the previous election as Saint John Park was part of the 4-member Saint John Centre riding at that time. We therefore look at the two succeeding elections. In 1978, the Liberals beat their provincewide showing in Saint John Park as well, but only by 2.6 percentage points. In 1982, the Liberals did 4.6 percentage points better in Saint John Park than they did provincewide. The average of these two comparable elections is a 3.6 percentage point lean to the Liberals, while the riding leaned 14.6 percentage points to the Liberals when Higgins was leader. We therefore calculate Higgins' leader bounce as 11.0 percentage points.

The analysis finds that 15 of the 17 men and women who have led one of the three major political parties into an election since 1974, have had a bounce on average. If we single out each election contest, of the 10 elections since 1974*, the 3 major party leaders have had a bounce 25 of 30 times. The two exceptions are Richard Hatfield, who underperformed what we assume a generic Tory would have done in Carleton Centre in 1978, 1982 and 1987 and Shawn Graham, who underperformed what we assume a generic Liberal (actually, not that generic as the comparator is his father) would have done in 2003 and 2006. Hatfield exceeded expectations in 1974, while Graham exceeded expectations in 2010. All other leaders have exceeded expectations versus their provincewide popular vote every time they've led their party to the polls.

So, it is clear to say that there is a leader bounce. Unpacking the numbers a bit, a few other potential conclusions can be observed:

  1. Liberal leaders tend to get smaller bounces than Conservative and NDP leaders. My conjecture on this is that because all 6 Liberal leaders since 1974 have run in ridings that lean Liberal to begin with, their potential voter pool is already somewhat saturated. Conservative leaders Dennis Cochrane and Bernard Lord ran in ridings that were then somewhat less Conservative-leaning than the province as a whole, as did NDP leaders John LaBossiere and Roger Duguay.
  2. Liberal and Conservative leaders tend to get their biggest bounce in their first election as leader, while NDP leaders tend to see their bounce grow over time.
  3. While Liberal leaders tend to have the same-sized bounce whether they win or lose the election, Conservative leaders actually do better in their home riding relative to the provincewide performance of their party when losing the election than when they win. Thus, it is more likely for a Liberal leader to lose his or her seat when being swept out of office than a Conservative, though this has not happened in recent history.

These conclusions should all be taken with a grain of salt. The whole analysis is based on 30 cases, which is a very small sample size. The three observations above are drawn from subsets of that already small sample. However, I believe that there is a compelling enough case to adjust for the presence of the leader. I have applied an "anti-leader bounce" to past ridings in elections where a leader was a candidate, and have in turn applied an appropriate leader bounce to the five ridings being contested to the party leaders in 2014.

*I thought I would explain why I only went back to 1974 for those who were interested, but it was too long a tangent to include in the main body of the post. Prior to that, analysis is difficult if not impossible as multi-member ridings were in place and calculating voting trends is very difficult. New Brunswick used the block voting system prior to 1974 in most ridings. Under this system, many ridings returned more than one member and each voter had as many voters as his riding had members. For instance, a voter in Gloucester County could cast 5 votes, while a voter in Campbellton could cast only 1. Thus, it is impossible with the data available to calculate the popular vote (that could only be done by examining every individual ballot). Moreover, as voters were not required to cast all of their votes (our Gloucester voter could have chosen to vote for 1, 2, 3, 4 or 5 candidates) and they could split their ballot (that is to say our Gloucester voter might have case 2 ballots for Liberals, 2 ballots for Conservatives and 1 for an NDPer). Due to this additional complication, it is impossible attempt to accurately transform the votes into a form that could compare with the popular votes in single member ridings after 1974.

Adjustments: A Hand Up for Incumbents

I've also done some research on whether or not the "incumbency factor" exists in New Brunswick elections. I looked at the 1978, 1982, 1987, 1991, 1999, 2003 amd 2010 elections (all elections where the previous election was fought under the same boundaries). In those elections, it showed that on average incumbents did about 6 points better than non-incumbents controlling for the regular partisan advantage within their ridings. This worked out to be virtually the same for Liberals and Conservatives. I also looked at the 1995 and 2006 elections to determine whether or not this holds true when the incumbent is running in a riding with significant portions that he or she has not previously represented. In these cases it looks like incumbents do on average 4 points better. I have applied a five point "bonus" to incumbents, including in cases where there are two incumbents in the same riding (meaning they have no relative advantage over each other, but they do over minor parties).

Effectiveness: How Would Have it Worked?

I plugged the popular vote results for the last 5 elections into the model as a test. It called the overall seat total correctly in the 2006 election, missed by no more than 1-2 seats per party in 1999 and 2003, and no more than 3 seats per party in 1995 and 2010. The incubmency factor was not in play in these tests and may have improved the results. In any event, if the polls are correct (always a big if), it seems this model should come fairly close to the seat totals as the election approaches.

I will begin using this seat model with the CRA poll to be released later today.