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Archive for the ‘Election Simulation’ Category

One of the first things you must decide upon when working on a MC simulation is the granularity of the simulation.

In particle physics the simulation would normally be at the level of the leptons, hadrons and photons we can see in the detectors, or perhaps even at the level of quarks if you are simulating plasma or collisions at higher energies.

There is a tradeoff, though, between accuracy at small scales and other factors such as computing power, data size, and also access to the raw data you need to run the model.  It wouldn’t make sense to try to simulate the weather or a tsunami at the quark-level, for example. Instead you would carve the atmosphere or the ocean up into an appropriately sized grid with granularity anywhere from a hundred meters-or-so up to tens of kilometers.

We have similar issues when trying to simulate election results, and there are a handful of fairly obvious choices for the granularity of the simulation.

  1. Nationwide: basically take the polling averages (with or without considering any margins of error) and assume that that is how the party votes will fall.  Throw in reasonable assumptions about which party’s candidates will win in Epsom, Ohariu, and the seven Maori electorates and you’ve got your result.  This is a good solution if you just want a rough guess at which side will form the government, and it is the level of reporting you typically get from the media and the blogs whenever a new poll is released.
  2. Electorate and candidate-level: This is a little more complicated.  Ideally you would want polling for each electorate, but even without that you can do an alright job by using the relative differences in results between electorates from a previous election.  This will cause problems when electorate boundaries change, however, so while it might have worked alright for the 2011 election it is a bit of a dodgy proposition for 2014.
  3. Polling place-level: The New Zealand Electoral Commission publish polling place analysis by electorate for both the party vote and the electorate candidate vote, helpfully in CSV format as well as HTML.  As with an electorate-level or candidate-level simulation you can do an acceptable job by using the relative differences in results between polling places from a previous election.  Difficulties occur when polling places are discontinued or new polling places are added between elections, and also when there is significant migration, such as that which occurred in and around Christchurch after the 2011 Christchurch Earthquake.
  4. Voter-level: Very handy if you are a political party and you want to tailor campaign material and get-out-the-vote efforts at specific individuals.  In fact, the Obama 2012 campaign data team is well known for performing simulations and doing analysis at this level of granularity. Many New Zealand libraries have copies of the Habitation Directory Habitation Index, which is the electoral role from the most recent 2011 General Election ordered by address.  Assuming you could get your hands on a digital copy then it is at least theoretically possible to geomap individual voters and make reasonable assumptions about their education, income, where they voted and who they voted for, albeit with a lot of attenuation bias.  Unfortunately if that is all the information you have to work with then that is about where you would get stuck.  If you had access to poll results with voting preferences for each person polled then things could start to get interesting, but for obvious reasons only the aggregate polling results are made available to the public.  I wouldn’t be surprised to see the two major parties working on this level of analysis and undertaking highly targeted messaging a few election cycles down the track, but I don’t think anybody in New Zealand is there yet.  Having said that, see the photo in this tweet from @somewhereben for evidence that MPs and volunteers knocking doors are already working to get their hands on some of the voter-level information that will be needed to pull this off.

I still haven’t made a final commitment to what level granularity to work at, but in the mean time I’m playing around with the polling place results try and see if we can understand what happens to voter turnout between elections at that level.  Hopefully the turnout at each polling place will be reasonably constant over time.

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Final effective party lists for the 2011 NZ General Election, based on candidate election probabilites post below.

This lists order candidates for each party by the probabilty of being elected to parliament as the lowest ranked successful list candidate for their party. In other words, the probability that a party vote for this party will go towards electing this candidate.

For more information please refer to the original effective party lists post.

Effective party list for the National party.

Effective party list for the National party.

A vote for the National party is a vote for Joanne HAYES (41%), Claudette HAUITI (35%), Sam COLLINS (14%), or Aaron GILMORE (5%).

Effective party list for the Labour party.

Effective party list for the Labour party.

A vote for the Labour party is a vote for Deborah MAHUTA-COYLE (36%), Stuart NASH (24%), Rick BARKER (24%), Carmel SEPULONI (7%) or Brendon BURNS (6%).

Effective party list for the Green party.

Effective party list for the Green party.

A vote for the Green party is a vote for David HAY (63%) or James SHAW (35%).

Effective party list for the ACT party.

Effective party list for the ACT party.

A vote for the ACT party is a vote for Don Brash (71%) or Catherine ISAAC (26%).

Effective party list for the Maori party.

Effective party list for the Maori party.

A vote for the Maori party is a wasted vote, in the sense that it will not help elect anybody to parliament because of the Maori party overhang.

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Shown below are the updated Candidate Election Probabilities based on tonight’s polling update. Please click to embiggen. For an explanation of the methodology please see the original post on individual candidate election probabilities.

(Should also point out that I’ve made a couple of manual tweaks to the list this time, as it is the last one to be published before the election. I have given the Progressive party’s votes in Wigram to the Labour candidate, who is widely considered to be the most likely to benefit from Jim Anderton not standing, and have given votes to Hone Harawira in Te Tai Tokerau to reflect his likelihood of winning there.)

  1. Rank: From 0 to 899, gives the respective candidate’s relative likelihood of being elected, and is ordered firstly by probability to be elected, and then by party code and list ranking where there is a tie.  Candidates are shown in the table ordered by “rank”.
  2. Party Code : A unique code for each political party.  Parties are numbered 0~7, and ordered firstly by the number of seats won in the 2008 NZ General Election, and secondly by the number of party votes received.
  3. Party
  4. List Ranking
  5. Name: The name of the candidate (as given on the Elections New Zealand website, where available).
  6. Electorate: The electorate the candidate will stand in. For list-only candidates this will read “list only.”
  7. Electorate Code : A unique code for the electorate.  Electorates are numbered in alphabetical order, with general electorates (#0 ~ #62) preceding Maori electorates (#63 ~ #69). If the candidate is a list-only candidate candidate this code will take the value -1.
  8. Elect. 08: Blank, for the moment.
  9. Prob. Electorate: Probabilty of being elected to parliament as an electorate candidate.
  10. Prob. List: Probabilty of being elected to parliament as a list candidate.
  11. Prob. Combined: Combined probabilty of being elected to parliament as an electorate candidate.
  12. Prob. Last: Probabilty of being elected to parliament as the lowest ranked successful list candidate for their party.  In other words, the probability that a party vote for this party will go towards electing this candidate.
Probabilities for each candidate to be elected to Parliament

Probabilities for each candidate to be elected to Parliament through their electorate, through the party list, and the overall combined probability. (PNG, 760kB)

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Shown below are the updated Candidate Election Probabilities based on tonight’s polling update. Please click to embiggen. For an explanation of the methodology please see the original post on individual candidate election probabilities.

Probabilities for each candidate to be elected to Parliament through their electorate, through the party list, and the overall combined probability.

Probabilities for each candidate to be elected to Parliament through their electorate, through the party list, and the overall combined probability. (PNG, 770kB)

Will follow tomorrow with some analysis, but for the mean time there are two points that stand out:

  1. With the number of recent polls the margins of error on the polling averages has shrunk, meaning there are less candidates on the above list.  There are only about 140 or so candidates with a chance of winning a seat, so if the polls are correct there won’t be too many surprises on election night.
  2. The results for Labour (but not so much for National) are heavily dependent on the electorate results, which aren’t necessarily modelled realistically given that National are polling so much higher than they were at either of the two previous general elections.  Many of Burns (#29, Christchurch Central), Tirikatene (#45, Te Tai Tonga), Hipkins (#42, Rimutaka), Lees-Galloway (#37, Palmerston North), Wood (#32, list only), Chadwick (#34, Rotorua), O’Conner (West Coast-Tasman, electorate only) and Sutton (#35, Waikato) are in for a disappointing night, but it’s difficult to tell exactly which at the moment.  For more info see Kiwiblog.

Will calculate the effective party lists tomorrow before the 12PM blackout, but for the moment they look as follows:

  1. National: Hayes (#64, Dunedin South), Hauiti (#63, Mangare), Collins (#66, Wigram)
  2. Labour: Nash (#27, Napier), Burns (#29, Christchurch Central), Mahuta-Coyle (#26, Tauranga)
  3. Green: Shaw (#15), Hay (#16)

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There has been a bit of hysteria the last few days about dire consequences if New Zealand First should be returned to parliament. See PM John Key on Stuff, or the Vote For Change campaign’s highly ignorable press releases, for example.

So what’s going on? A couple of recent polls have the NZF party closing in on the 5% threshold, and the probability of NZF being returned to Parliament has shot up to about 50% on iPredict, from about 15% just over a week ago.

Probability of New Zealand First being returned to parliament according to iPredict, as of evening of 20 November, 2011.

Probability of New Zealand First being returned to parliament according to iPredict, as of evening of 20 November, 2011.

On top of this, NZF leader Winston Peters has made a point of saying he won’t go in to coalition with anybody, or support anybody with supply and confidence, leading observers to assume that if NZF wins seats in parliament this election everything will turn to custard and we will be having another election in the next few months.

So what would actually happen if NZF were returned to parliament?

The current situation.

To figure this out we run a series of simulations, firstly based on the current polling avereges. We call this “Situation #0”. It looks something like this:

Histogram showing the total number of seats National are expected to win in parliament under Situation #0. National are expected to win 65.4 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats National are expected to win in parliament under Situation #0. National are expected to win 65.4 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats Labour are expected to win in parliament under Situation #0.  Labour are expected to win 35.4 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats Labour are expected to win in parliament under Situation #0. Labour are expected to win 35.4 +/- 0.8 (RMS) seats.

Keep in mind that a party would need 63 seats to win a majority:

Histogram showing the number of seats needed to form a majority in Parliament under Situation #0. The winning party or coalition will most probably need 63 seats in Parliament to form a majority.

Histogram showing the number of seats needed to form a majority in Parliament under Situation #0. The winning party or coalition will most probably need 63 seats in Parliament to form a majority.

So National is therefore almost guaranteed an outright majority in the house:

Scenario analysis for Situation #0. The bar graph shows the probabilities for different possible outcomes for a NZ General Election.  The National Party would have a roughly 99.98% chance of governing alone, a roughly 0.02% chance of governing as leader of a National-ACT coalition, and a 0% chance of governing as leader of a National-ACT-United Future coalition. There is a 0% chance that the Maori Party would hold the balance of power in Parliament.

Scenario analysis for Situation #0. The bar graph shows the probabilities for different possible outcomes for a NZ General Election. The National Party would have a roughly 99.98% chance of governing alone, a roughly 0.02% chance of governing as leader of a National-ACT coalition, and a 0% chance of governing as leader of a National-ACT-United Future coalition. There is a 0% chance that the Maori Party would hold the balance of power in Parliament.

So there you have it.

What if NZF makes 5%?

And what would happen if NZF just makes the 5% threshold? Firstly lets simulate this by assuming that NZF takes the same number of votes from National and Labour such that they get exactly 5%. We call this “Situation #1”. Under Situation #1 NZF would win exactly 6 seats. And the other parties?

Histogram showing the total number of seats National are expected to win in parliament under Situation #1. National are expected to win 62.1 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats National are expected to win in parliament under Situation #1. National are expected to win 62.1 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats Labour are expected to win in parliament under Situation #1. Labour are expected to win 33.2 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats Labour are expected to win in parliament under Situation #1. Labour are expected to win 33.2 +/- 0.8 (RMS) seats.

So with NZF taking 1% or so of the vote from each of National and Labour and winning 6 seats, National and Labour would respectively be 3.3 and 2.2 seats worse off. The fallout is not just limited to those two parties either; the Greens, for example, would be 0.5 seats worse off. And who would form the government?

Scenario analysis for Situation #1. The bar graph shows the probabilities for different possible outcomes for a NZ General Election.  The National Party would have a roughly 25.1% chance of governing alone, a roughly 70.5% chance of governing as leader of a National-ACT coalition, and a roughly 4.1% chance of governing as leader of a National-ACT-United Future coalition. There is a 0.3% chance that the Maori Party would hold the balance of power in Parliament.

Scenario analysis for Situation #1. The bar graph shows the probabilities for different possible outcomes for a NZ General Election. The National Party would have a roughly 25.1% chance of governing alone, a roughly 70.5% chance of governing as leader of a National-ACT coalition, and a roughly 4.1% chance of governing as leader of a National-ACT-United Future coalition. There is a 0.3% chance that the Maori Party would hold the balance of power in Parliament.

So if NZF takes votes off National and Labour equally and makes the 5% threshold there is a much reduced chance of National getting a majority, but we would still have a National Prime Minister. Winston Peters wouldn’t be in a position to force another election.

What if the votes come exclusively from National?

And what would happen if NZF just makes the 5% threshold, and takes their extra votes exclusively from current National supporters. We call this “Situation #2”. Under Situation #2 NZF would still win exactly 6 seats, and National would be as follows:

Histogram showing the total number of seats National are expected to win in parliament under Situation #2. National are expected to win 61.2 +/- 0.8 (RMS) seats.

Histogram showing the total number of seats National are expected to win in parliament under Situation #2. National are expected to win 61.2 +/- 0.8 (RMS) seats.

Scenario analysis for Situation #2. The bar graph shows the probabilities for different possible outcomes for a NZ General Election. The National Party would have a roughly 4.4% chance of governing alone, a roughly 69.6% chance of governing as leader of a National-ACT coalition, and a roughly 21.1% chance of governing as leader of a National-ACT-United Future coalition. There is a roughly 5.0% chance that the Maori Party would hold the balance of power in Parliament (with a National-coalition advantage).

So if NZF takes votes solely off National and just makes the 5% threshold there is a much reduced chance of National getting a majority, but we would still most likely get a National Prime Minister, even without taking the Maori Party into consideration. Winston Peters almost certainly wouldn’t be in a position to force another election.

What if NZF makes 7%, and the votes come exclusively from National?

Now lets assume that NZF wins exactly 7% of the vote, with their extra votes coming exclusively from current National supporters. We call this “Situation #3”. Under Situation #3 the results would be as follows:

Histogram showing the total number of seats NZF are expected to win in parliament under Situation #3. NZF are now expected to win 8.7 +/- 0.4 (RMS) seats.

Histogram showing the total number of seats NZF are expected to win in parliament under Situation #3. NZF are now expected to win 8.7 +/- 0.4 (RMS) seats.

Histogram showing the total number of seats National are expected to win in parliament under Situation #3. National are expected to win 58.6 +/- 0.7 (RMS) seats.

Histogram showing the total number of seats National are expected to win in parliament under Situation #3. National are expected to win 58.6 +/- 0.7 (RMS) seats.

Scenario analysis for Situation #3. The bar graph shows the probabilities for different possible outcomes for a NZ General Election.  The National Party would have a 0% chance of governing alone, a roughly 0.4% chance of governing as leader of a National-ACT coalition, and a roughly 4.5% chance of governing as leader of a National-ACT-United Future coalition. There is a roughly 95.5% chance that the Maori Party would hold the balance of power in Parliament (still most likely with a National-coalition advantage).

Scenario analysis for Situation #3. The bar graph shows the probabilities for different possible outcomes for a NZ General Election. The National Party would have a 0% chance of governing alone, a roughly 0.4% chance of governing as leader of a National-ACT coalition, and a roughly 4.5% chance of governing as leader of a National-ACT-United Future coalition. There is a roughly 95.5% chance that the Maori Party would hold the balance of power in Parliament (still most likely with a National-coalition advantage).

So even under the rediculously optimistic scenario of NZF doubling their current support in the next six days, with the new support coming solely off National, the Maori party would still most-likely hold the balance of power in parliament.

And what would the Maori party do? Coalition with National, ACT and United Future? Or coalition with Labour, Greens, Mana and New Zealand First? Even assuming that the latter four parties were all on the same page (unfeasible, given recent statements from their leaders), would the Maori party favour them? Not likely if a three-party right-wing coalition had a numbers advantage over the four-party left-wing coalition. It would be far too easy (politically) for the Maori Party to go into a right-wing coalition, and extract some fairly heavy concessions whilst doing so.

Conclusion.

So, in summary, even if NZF win 7% of the vote, which is unlikely on current polling, the chances of them holding a balance of power and forcing another election are effectively zero. Anybody who suggests otherwise is just being a bit hysterical.

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When I started the blog a couple of years ago I sort of promised to write a series of posts on how the simulation works so that others could replicate the results, if need be. Unfortunately gainful employment has interfered, and one week out from the election there is no way I will get this finished. Still, better late than never.

While there is a bit of maths going on behind the scenes, the general principle is surprisingly simple: average all available NZ political polls, and then run a Monte Carlo Simulation to get all the interesting information we need to make the graphs. This process is summarised in the schematic below:

General overview of poll averaging and election simulation.

General overview of poll averaging and election simulation.

The process can be divided up in to 3 main steps:

  1. Polling information (red): Moving averages of the political polls and information regarding electorate swings are calculated from the input polls and the results of the 2005 and 2008 General Elections. (NB, this information, along with the party lists in step 3, is the only information that goes in to the calculations.)
  2. Election simulation (blue): Using the Monte Carlo method, running on a standard laptop with a standard pseudo-random number generator, an election is simulated, based on the polling averages and electorate swings calculated in step 1.
  3. Scenario analysis (green): Using the simulated election results from step 2, we look at the party lists and figure out who gets in to parliament.  We then look at any other result that may be of interest.  Normally this would be the number of seats won be each party, which parties will form a coalition and so on, but in theory, if the simulation in step 2 is working correctly, it can be anything you may be interested in looking at after a real election.  For example, if you wanted to, you could look at the number of women candidates winning a South Island electorate seat.

Of course, depending on the pseudo-random numbers dished up in step 2 you may get a relatively unlikely result: perhaps based on current polling your simulation gives National 47% of the vote, Labour 32%, Greens get 14%, and New Zealand First 5%.  This is possible, but not the most probable outcome.  To make sure the results are realistic we simply repeat steps 2 and 3 a large number of times, and keep a running total for each variable or outcome we are interested in measuring.  By doing this any unlikely statistical fluctuations should cancel each other out, and we can get a meaningful measurement of the numbers we are interested in.

Typically steps 2 and 3 are repeated 50,000 times for each day we simulate an election for, which takes about a minute or so of computer time.  To get the time series graphs, we have to do these simulaitons for each day we are interested in, although normally they are just run for the last couple of hundred days to update any recent movement, such as the Scenario Analysis time series graph, for example (scroll down to “Scenario Analysis”).

Each time we complete step 3, we update a running total of the variables we are interested in (number of seats won by National, number of women candidates winning a South Island electorate seat, etc.) and also the variables-squared (number of seats won by National squared, number of women candidates winning a South Island electorate seat squared, etc.). We then divide by the total number of simulations (say, 50,000) and that gives the expected values and expected value-squareds. For example, in yesterdays simulations the National party won 3,270,000 seats, and dividing by 50,000 gives an expected value of 65.4 seats. A bit of seventh-form stats gives the root mean square (RMS) error on the expected value, and that is how we get the final value of 65.4 +/- 0.8 seats for National (scroll down to “Seats in Parliament”).

That’s all there is to it. The calculations for the poll averaging and the simulation get a bit more involved, although probably not much harder than a first-year uni level maths course, but the general principle of the calculation should be surprisingly simple.

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There has been a bit of talk lately about tactical voting in Epsom, and the “cup of tea” between PM John Key and ACT Epsom candidate John Banks has been in the news a bit.  So what’s going on?

The short version of the story is that in New Zealand, where we elect our Parliament under MMP, a party needs to either win 5% of the nationwide popular vote (party vote) or win an electorate seat to get seats in Parliament in proportion to their party vote. The current National party government’s coalition partner, the ACT party, won’t make the 5% threshold on current polling, and so the PM is in a position where he is motivated to throw the ACT party an electorate seat, the seat of Epsom to be precise.

So what happens if ACT do win Epsom?

Total seats won by ACT party, assuming they win Epsom.

Total seats won by the ACT party, assuming ACT win Epsom.

Total seats won by National party, assuming ACT win Epsom.

Total seats won by the National party, assuming ACT win Epsom.

This is the more likely situation at the moment: ACT win 1 electorate and 2.0 +/- 0.1 (RMS) total seats in Parliament. Under this scenario the National party would win 65.4 +-/ 0.8 (RMS) seats in parliament.

And what happens if ACT don’t win Epsom, and the National party candidate (Paul Goldsmith) wins instead?

Total seats won by ACT party, assuming National win Epsom.

Total seats won by the ACT party, assuming National win Epsom.

Total seats won by the National party, assuming National win Epsom.

Total seats won by the the National party, assuming National win Epsom.

In this situation the ACT party gets no seats in Parliament, and is 2.0 +/- 0.1 seats worse off. The plus-side for National is that they win 66.5 +/- 0.8 seats, and are now 1.1 seats better off.

You can do similar calculations for the other parties.  Here’s how everybody ends up if National win Epsom, relative to how they would have been if ACT had won Epsom:

  • National: +1 electorate seat, +0.1 list seats.  Overall +1.1 seats better off.
  • Labour: +0.6 seats.
  • Green: +0.3 seats.
  • ACT: -2.0 seats.
  • Maori: +0.0 seats.
  • NZF: +0.0 seats.
  • Overhang: +0.0 seats in Parliament.
  • (NB: rounding)

For those who wonder why Labour only gets 0.6 extra seats, vs. National’s 1.1, the answer is simple: Labour is polling just over half what National is polling in terms of the party vote. Regardless, if you ignore the probability of ACT going into coalition with Labour, Labour are still better off if National win Epsom than they are if ACT win Epsom.

This raises interesting questions regarding tactical voting for those in the Epsom electorate. Assuming that ACT will not hold a balance of power after the election and choose to go in to coalition with Labour, then Labour are better off if Paul Goldsmith (National candidate for Epsom) wins the seat, and John Banks (the ACT candidate) loses. Similar logic applies for the Greens, Mana, and NZF. ACT supporters obviously want their candidate to win. For Maori, United Future and National supporters the situation is a bit more complex, and depends on who is likely to win the election.

For that, please refer to the scenario analysis graphs below:

Scenario analysis for the most recent election simulation assuming ACT win Epsom.

Scenario analysis for the most recent election simulation assuming ACT win Epsom.

Total seats won by the the National party, assuming National win Epsom.

Total seats won by the the National party, assuming National win Epsom.

Looking at the two graphs, you might not notice too much difference. The first graph shows National with a 99.98% chance of winning a majority, and a 0.02% chaince of leading a National-ACT coalition. The second shows National with a 100.00% chance of winning an absolute majority, and a 0.00% chance of leading a National-ACT coalition. Either way, New Zealand gets a National Party Prime Minster.

So if you are a National, Maori or United Future party supporter, what is your preferred result? Based on current polling it would be option #2 above: National win Epsom.

(I should here point out the difference between tactics and strategy. On this blog, “tactics” refers to the short term: doing what is necessary to get the result you want from the next election. “Strategy” refers to a more long-term positional advantage. Pollsters are not in a position to comment on whether having ACT in Parliament would be good or bad for National, Maori and United Future supporters in the long term.)

The results of this hypothetical analysis are surprisingly simple: Labour, Green, Mana and New Zealand First supporters in Epsom, and an overwhelming majority of National, Maori and United Future supporters in Epsom should vote tactically for Paul Goldsmith. The National candidate should win in a landslide.

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[Update: Election results available on the Electoral Commission website.]

The 2011 Te Tai Tokerau by-election will be held today. This is the fourth by-election to be held since the 2008 general election, which, whilst not a record, is certainly the most during the last ten terms of parliament.

To date I am aware of only one poll in the electorate, which was the Native Affairs-Baseline poll which had Hone Harawira (Mana Party) on 41%, Kelvin Davis (Labour Party) on 40% and Solomon Tipene (Maori Party) on 15%.

As with the previous 2009 Mount Albert by-election, 2010 Mana by-election and 2011 Botany by-election I have attempted to predict the outcome of the election and the share of the votes won by each of the major or minor NZ political party’s candidates using a Monte Carlo simulation of 50,000 NZ general elections based on recent political polling results. The results for the Te Tai Tokerau by-election are determined using the Uniform National Swing model of electorates. The results of the simulation are shown in the table below, and the results of the 2008 General Election for the Te Tai Tokerau electorate are included for reference.

Simulated results of 2011 Te Tai Tokerau by-election

Table showing simulated results of 2011 Te Tai Tokerau by-election, as calculated on 25 June 2011.

So that is a guaranteed win for Solomon Tipene and the Maori Party!

It goes without saying that the whole prediction is an excercise in futility given that the recently-formed Mana Party didn’t exist at the previous election, and so we don’t have any baseline off which to predict their performance. In fact the discrepancies with the one opinion poll quoted above are so great that, unlike the recent Mana and Botany by-elections, the simulation has practically no predictive power whatsoever. It isn’t even obvious what would count as a “good” result for each of the candidates (although winning the by-election should probably be considered a “good” result). I guess this post therefore serves as another warning against taking the results of Uniform National Swing predictions too seriously.

The only other quantitative predictions for the Te Tai Tokerau by-election that I’m aware of are from New Zealand futures market iPredict, who as of 17:50 (see screen captures below) are giving the Mana Party a 78.0% chance of winning, the Labour Party an 18.7% chance of winning, and any other candidate a 2.0% chance of winning (probabilities do not necessarily have to add to 100% due to the bid/ask spread). iPredict also predict that the Mana Party candidate will win 43% of the vote, the Labour Party candidate will win 41% of the vote, the Maori Party candidate will win 17% of the vote.

I’m not aware of anybody else making quantitative prediction on the results, but if you know of anybody, or if you would just like to take a punt, then feel free to leave a comment below.

iPredict's Te Tai Tokerau by-election winner predictions

Screen capture of iPredict's Te Tai Tokerau by-election winner predictions, as of 17:50 on 25 June 2011.

iPredict's Te Tai Tokerau by-election vote share predictions

Screen capture of iPredict's Te Tai Tokerau by-election vote share predictions, as of 17:50 on 25 June 2011.

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When I first published a post on the probabilities of being elected on a candidate-by-candidate basis last year I mentioned that the main motivation was that I hoped that people will be able to see which individual list candidate their party vote is likely to be counted for.

Closer to the 2011 General Election I will begin publishing “effective party lists” on a regular basis. These effective lists will show only those candidates on the cusp of winning a list seat for each party, and will hopefully give NZ voters a better idea of where their vote is going, and a more meaningful alternative to a quick glance at the top of the lists for each party which some seem to use now when deciding how to cast their votes.

I think this is still quite important information, and I want to make sure it is available publicly immediately before the 2011 General Election so that people can make a more-informed party vote. But recently another benefit has become obvious: helping parties to avoid the so-called “Tizard Problem.” Since Darren Hughes announced his resignation last week there has been speculation that Labour will ask the next highest placed list candidate, Judith Tizard, to stand aside in order to allow a lower ranked list candidate to filter through to Parliament. There were also suggestions on some blogs that the party didn’t want to stand list MPs in the by-elections for safe Labour seats in Mana and Mt Albert because that would have allowed Tizard back into Parliament, thus limiting their options for candidate selection for the by-elections.

I’m not sure how accurate these theories are of what the Labour Party strategists are actually thinking, and I’m not going to speculate, but if they are true, then they represent a massive failure on the part of those who determined the Labour Party List for the 2008 Election.

After a bit of thought I’ve decided that preventing a hypothetical “Tizard Problem” basically just involves figuring out the effective party lists for each of the parties. Specifically, figuring out who your party vote is going to help get elected is simply a case of figuring out who the lowest ranked list candidate to win a list seat for the party that you voted for is. And this is basically the same problem as figuring out who the highest ranked list candidate to not be awarded a seat is. This can be calculated from the results of the election simulation we use here to figure out which candidates get in to Parliament, and which miss out. The methodology is the same as that for the other simulations on this site.

By simulating a large number of elections based on current opinion polling, and counting up the number of times each party list candidate is the lowest-ranked list candidate to be elected for their party, we can see who the party votes for each party are going towards electing. The results are shown below for each of the eight major and minor NZ political parties, with the probability of a candidate being the lowest-ranked list candidate to be elected for their party shown under the heading “Prob. Last” in the right-most column. The effective party lists are ordered by decreasing values of “Prob. Last.” The party list rankings of the candidates shown at the tops of these lists correspond to the “sweet spots” on each respective parties list, in other words, the list rankings that could potentially result in a “Tizard Problem” for those parties during the next term of Parliament if they were to be filled by electorally unpopular candidates.

The first example is for the Green Party, one of the easier results to understand.

Effective party list for the Green Party

Effective party list for the Green Party.

First place on the Green Party effective party list is Steffan Browning, with list ranking #9 and standing in the Kaikoura electorate. He has a 0% chance of winning his electorate seat, a 79% chance of getting in on the list, and a 32% chance of being the lowest ranked Green party candidate to be elected. In other words, if you vote for the Green party with your party vote there is a 32% chance that your vote will go towards electing Browning. The effective party list then skips up and down the actual party list, with Mathers (list ranking #10), Hughes (#8) and Ward (#11) following. The reason Hughes (#8) is below Browning (#9) is because whilst he is slightly more likely to be elected, he is less likely to be the last person elected. For the same reason, highly-ranked list candidates such as co-leaders Metiria Turei and Russel Norman are almost guaranteed to be elected whether you vote for the Greens or not, and thus have low effective party list rankings of #10 and #11, respectively.

If you add up the numbers for “Prob. Last” in the far right column you will get 100% (give or take a bit of rounding error), which means there is a 100% chance that your party vote for the Green Party will go towards getting somebody elected from their list.

Next up is the Maori party.

Effective party list for the Maori Party

Effective party list for the Maori Party.

Nothing interesting is happening here, with the effective party list exactly matching the order of the actual party list, and candidates either winning an electorate seat or not being returned to Parliament. This is because of the overhang caused by the Maori Party, with the party winning more electorate seats than the total number of seats they would be entitled to based on their party vote.

If you add up the numbers for “Prob. Last” in the far right column you will get 0%, which means there is a 0% chance that your party vote for the Maori party will go towards getting somebody elected from their list. In other words, a party vote for the Maori Party is a guaranteed “wasted” vote.

The examples for both the Green and Maori parties are easy enough to understand intuitively, but things get a bit more complicated when you look at parties that may win both electorate and list seats, such as the ACT party.

Effective party list for the ACT Party

Effective party list for the ACT Party.

First up is John Boscawen, with a 31% chance of being the lowest ranked list candidate elected, followed by Roger Douglas (5%) and Heather Roy (0%, rounded down). In fourth place on the effective list is party leader Rodney Hide, with 0% chance of being the lowest ranked candidate. The reason for this is that ACT Party Leader Hide, like Maori Party leader Pita Sharples, will either win his electorate seat or not return to Parliament. Unlike #2 – #4 on the ACT party list he has no chance of winning a list spot on current polling (where ACT are well below the 5% threshold).

If you add up the numbers for “Prob. Last” in the far right column you will get 36%, which means there is a 36% chance that your party vote for the ACT party will go towards getting somebody elected from their list. In other words, there is a 74% chance that a party vote for the ACT party will be a wasted vote. More specifically, there is a 4% chance that a party vote for the ACT party will be a wasted vote because Hide will lose Epsom and nobody from ACT will be elected, and there is a 70% chance that a party vote for the ACT party will be a wasted vote because although Hide wins Epsom, the party does not get enough party votes for somebody else to join him as a list MP.

The three patterns above explain most of the possible outcomes as far as effective party lists go, and for the other parties the effective party lists just behave as a combination of the patterns seen above. Next is National:

Effective party list for the National Party

Effective party list for the National Party.

The sweet spot on the list here belongs to Ravi Musuku (Mt. Albert, list ranking #63), Mita Harris (Mangere, #62) and Marc Alexander (Wigram, #60). These are the people your party vote will be going towards getting elected if you party-vote National.

What happened to those on the list ranked #61 (Malcolm Plimmer) and #64 (Jonathan Young)? They’re on the effective list as well, just a bit further down. The reason is that for them to be the lowest ranked National candidates to win a list seat they would have to first lose their electorate seats, New Plymouth and Palmerston North, which are National-leaning seats. (Yes, I’m aware that New Plymouth and Palmerston North are not traditionally considered “National-leaning seats.” The individual electorate results are modeled on the principle of Uniform National Swing). This is why you have to take the results in individual electorate seats into account when trying to figure out where your party vote is going!

Next is the Labour Party:

Effective party list for the Labour Party

Effective party list for the Labour Party.

A vote for the Labour Party is most likely going to go to Damien O’Conner (West Coast-Tasman, #32), Grant Robertson (Wellington Central, #34), or Iain Lees-Galloway (Palmerston North, #36). All three face a difficult battle to win their electorate seats on current polling.

Judith Tizard is still on the effective party list in #9 position, with a 5% chance of being the lowest ranked Labour list candidate to win a list seat in Parliament.

Next up, the Progressive Party and the United Future Party:

Effective party list for the Progressive Party

Effective party list for the Progressive Party.

Effective party list for the United Future Party.

Effective party list for the United Future Party.

These two show a pattern very similar to that shown by the ACT Party. In all three cases you have a party leader with a non-100% chance of winning an electorate seat, and a party that is not guaranteed to break the 5% threshold to get seats without the electorate waiver, which results in a non-zero possibility of a wasted vote. In all three cases the wasted vote can be caused by the leader failing to win their electorate seat, or by winning their electorate seat but the party not having a high enough party vote to elect other list MPs along with them.

Finally, the New Zealand First Party.

Effective party list for the New Zealand First party

Effective party list for the New Zealand First party.

Another fairly intuitive result. With NZF polling about 4% at the moment, they are within a margin-of-error or so from breaking the 5% threshold, which, like the Green Party, would see them win list seats even though they are not predicted to win an electorate seat. The sweet spot on the NZF party list corresponds to candidates with list rankings of #6 and #7.

Obviously the results above are purely hypothetical, given that they are based on old party lists from the 2008 General Election that have been modified arbitrarily to take account of retirements and so on during the current term of Parliament. I look forward to whipping up new lists when the finalised party lists for the 2011 General Election are made public.

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The 2010 Mana by-election will be held today. Unfortunately, we haven’t seen any polling in the electorate, and national-level polling over the past few weeks has been sparse, so it’s not very obvious what to expect.

In spite of the problems mentioned above, I have attempted to predict the outcome of the election and the share of the votes won by each of the major or minor NZ political party’s candidates using a Monte Carlo simulation of 50,000 NZ general elections held today based on recent political polling results. The results for the Mana electorate are determined using the Uniform National Swing model of electorates. The results of the simulation are shown in the table below, and the results of the 2008 General Election for the Mana electorate are included for reference.

Table showing simulated results of 2010 Mana by-election.

Table showing simulated results of 2010 Mana by-election, as calculated on 20 November, 2010.

For reference, similar predictions and results for the 2009 Mt Albert by-election are shown in the table below. The results of the 2009 by-election are of course already known, so you’ll just have to take my word for it that they were not used to cheat by including them as inputs in the simulation.

Table showing simulated results of 2009 Mt Albert by-election.

Table showing simulated results of 2009 Mt Albert by-election, as calculated on 13 June, 2009.

As you can see, the predictions aren’t particularly brilliant. The simulation significantly underestimated the results for the Green Party, and overestimated the results for National. The results for Labour aren’t significantly out, but given that the flow of support was most probably National to Labour and Labour to the Greens, rather than National to the Greens directly, then this was probably just a lucky coincidence.

There are several likely possible causes for discrepancy:

  1. The UNS model for the electorate results is not reasonable.  Empirically, the model has performed well in median seats, but is not very realistic when used in party strongholds such as Mt Albert and Mana, which have historically been safe Labour seats.
  2. There is usually a swing against the government in by-elections relative to that which would be expected from national-level polling, something which the simulation doesn’t take into account.
  3. By-elections tend to attract a different selection of candidates than a general election typically would.
  4. By-elections tend to attract a different selection of voters than a general election typically would, with voter turnout affecting the result in unpredictable ways.

Given the above caveats, the predictions for Mana should be interpreted loosely.  I’m not going to take responsibility for them if they are significantly out, and conversely I will not be taking any credit if they prove accurate.

As for today’s Mana by-election, the only other predictions of the result of the election that I am aware of are from New Zealand futures market iPredict, who as of 15:40 (see screen captures below) are giving the Labour candidate a 96.99% chance of winning and the National a 2.36% chance of winning. iPredict also predict that the Labour candidate will win 46.67% of the vote, the National candidate will win 36.97% of the vote, and all others combined will win 16.80% of the vote. I’m not aware of anybody else making quantitative prediction on the results, but if you know of anybody, or if you would just like to take a punt, then feel free to leave a comment below.

iPredict Mana by-election winner predictions

Screen capture of iPredict's Mana by-election winner predictions, as of 15:40 on 20 November, 2010.

Screen capture of iPredict's Mana by-election vote share predictions, as of 15:40 on 20 November, 2010.

Screen capture of iPredict's Mana by-election vote share predictions, as of 15:40 on 20 November, 2010.

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