Feeds:
Posts
Comments

Archive for the ‘Scenario Analysis’ Category

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.

Advertisements

Read Full Post »

One of the major goals of this site is to try and predict election results based on recent relevant political polling. This is intended to include not just the total number of seats won by each party, but also viable coalition possibilities and electorate level results.

Today I present the simulation results at the candidate level, including probabilities for each major or minor party candidate to be elected to parliament by either winning an electorate or being selected off their party list. First though, in the interests of disclosure, I thought I should release the data I’m using for the party lists. The 2008 Party Lists are available in MS Excel (.xlsx) format [82kB].

The simulation requires the party lists to be input in the form of a list linking each candidate to the electorate they stood for (or else indicating they were a list only candidate.) The list is based largely on the information on the Party lists for the 2008 General Election page on the Elections New Zealand website, and the electorate information from the Candidates by electorate page from Wikipedia, and is amended at discretion.

The data format is as follows:

  1. 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.
  2. Party
  3. List Ranking
  4. Name : The name of the candidate as given on the Elections New Zealand website.
  5. Electorate : The electorate the candidate stood in. For list-only candidates this will read “list only.”
  6. 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.

For computational reasons each major or minor party candidate standing in an electorate must have a list ranking. In order to avoid having this requirement affect the results the lists are simply extended to 100 candidates for each party, with electorate-only candidates placed in the lowest ranked positions such that they will never be elected to a list seat. The intermediate positions are then filled with dummy candidates: for example, the candidate “NAT-74-list only” refers to the 74th ranked candidate on the National Party list, with the “list only” suffix indicating that they are a list-only candidate. Please feel free to use or amend the file at will. Corrections gratefully accepted.

The current simulation, however, does not use the 2008 Party Lists. Instead it references an alternative list that has been amended to take into consideration changes during the current term of Parliament. This current list used for the simulation is also available in MS Excel (.xlsx) format [82kB]. A summary of changes is as follows:

  1. Labour : The list reflects the retirements of Helen Clark and Michael Cullen during the term of Parliament. Candidates ranked #3 (Phil Goff) onwards are moved up two list places each. Current Parliamentary members are moved up in the list ahead of unsuccessful candidates (ahead of list candidate #42 Judith Tizard). A new candidate replacing Helen Clark (David Shearer, Mount Albert) is included, ranked #41 and inserted into the list ahead of Judith Tizard. A new dummy list candidate (“LAB-77-list only”) is inserted in position #77 in place of Michael Cullen.
  2. National : Richard Worth (unsuccessful candidate for Epsom, list rank #23) is removed, and subsequent candidates are moved up one rank. A new dummy candidate for Epsom (“NAT-67-Epsom”) is inserted in position #67 in his place.
  3. Green : Jeanette Fitzsimons (list-only candidate, list rank #1) and Sue Bradford (candidate for East Coast Bays, list rank #3) are removed, and subsequent candidates moved up. A new dummy candidate for East Coast Bays (“GRE-66-East Coast Bays”) is inserted in position #66 replacing Sue Bradford. A new dummy list candidate (“GRE-67-list only”) is inserted in position #67 in place of Jeanette Fitzsimons.

The above modifications are only intended to capture the spirit of changes since the beginning of the term of parliament and are of course subject to change when the parties release their official party lists closer to the date of the 2011 General Election. If anybody has any serious objections – or is just curious how things would work out with different party lists – and is willing to provide an updated list in the same format then I would be happy to rerun any simulations.

The candidate level results of the most recent simulation (January 22nd, after the release of the latest Roy Morgan Research poll) are shown in the table below (please click for an enlarged view.)

Probabilities for each candidate to be elected to Parliament

The table gives the probabilities for each candidate to be elected to Parliament by winning an electorate, by being elected from their party list, and an overall probability for either method combined. The “Rank” column 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. Probabilities are rounded to the nearest percent.

The first 89 ranked candidates are guaranteed to be elected, and will of course win 89 seats between them. Candidates ranked 90 through to 114 are considered highly likely to be elected, and each have individual probabilities in the 90% to 100% range. These 25 candidates are expected to win a further 24.6 seats between them, for a cumulative total of 113.6 seats in Parliament. After this we get to the marginal list and electorate candidates: those ranked 115 through to 135 have probabilities in the 10% to 90% range. These 21 candidates are expected to win a further 9.4 seats between them, for a cumulative total of 123.0 seats in Parliament. Next we have 14 more canadidates ranked 136 through to 149 who are considered highly unlikely to be elected to Parliament, with probabilities of less than 10% each. These 14 candidates are expected to win only 0.2 seats between them, bringing the cumulative total to 123.2 seats – an expected overhang of 3.2 seats. Finally, candidates ranked 150 through 800 (many not shown in the table for ease of viewing) have no chance of being elected to Parliament based on current polling data.

I realise that the above calculations may seem little more than trivia at the moment given that we are so far out from the next election, and that the finalised party lists and electorate candidates will not be known for a long time. However, the main motivation for doing this simulation is a hope 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.

Read Full Post »

In the last few posts we’ve looked at polling averages and the number of electorate seats and total seats won in Parliament by the various political parties. For most people, however, when looking at political polls the main result they are interested in is which party or coalition would win an election if it was held today.

To answer this question we use the same technique as we used to calculate the distributions of electorate seats: a Monte Carlo Simulation. Based on the latest polling averages we simulate a single election, figure out which party or coalition wins, and then repeat that process 10000 times to average out the statistical uncertainties. After that it is just a simple matter of counting up the results to get the probabilities. When we do this with the polling averages from the 20th November, after the release of the latest poll from Roy Morgan Research, we get the following results.

Scenario analysis for 20th November 2009.

Scenario analysis for 20th November 2009, listing the probabilities for different possible outcomes for a NZ General Election if held on that date.

As can be seen from the table, we calculate a 99.87% chance of National attaining an outright majority, and an additional 0.13% chance of a National-ACT coalition government. It is necessary though to clarify that the 0.13% does not necessarily mean that the result of an election would be a National-ACT government, rather it simply refers to the probability that National would not have enough seats to govern alone, but National and ACT between them would. Under these circumstances National and ACT might instead choose to form a broader coalition containing other parties, such as the Maori Party and United Future; or National may choose to ignore ACT and instead form a coalition with another party such as the Green Party; or ACT may instead choose to go into a grand coalition with all parliamentary parties except National. The only reason the table refers to a National-ACT coalition instead of one of these other possible results is that it is considered the most likely outcome based on the political reality of the relationships between the parties as of the present.

The information in the above table can alternatively be summarised as a bar graph, as shown below.

Scenario analysis for 20th November 2009.

Scenario analysis for 20th November 2009. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date. Results are identical to those in the table above.

This graph, however, isn’t particularly interesting, at least given the near certainty of a National Party absolute majority due to their current dominant lead in the polls. It may be more interesting to instead look at similar Scenario Analysis graphs from the dates of previous NZ General Elections.

Firstly, the predictions (retrodictions) for the 2008 General Election were (are) as follows:

Scenario analysis for 8th November 2008, the date of the 2008 NZ General Election. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date.

Here the most likely outcome (approximately 75% probability) is of a National-ACT coalition, which is in fact what happened; in the 2008 NZ General Election National’s 58 seats were not enough to govern alone, and they had to rely on the 5 seats from the ACT party to attain a majority. There is also a roughly 20% probability that National and ACT between them would need additional seat(s) from United Future to form a majority; and a roughly 5% probability that National, ACT and United Future would not hold enough seats between them to form a majority, and the Maori Party would hold the balance of power in parliament, albeit with the Center-Right coalition having a numerical advantage over the Center-Left.

Next, the predictions (retrodictions) for the 2005 General Election were (are) as follows:

cenario analysis for 17th September 2005.

Scenario analysis for 17th September 2005, the date of the 2005 NZ General Election. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date.

Here the near-certain outcome is for a four-way coalition between Labour, the Progressives, the Green Party and the New Zealand First Party, which again is what happened in the 2005 NZ General Election, or at least what would have happened if the parliamentary parties were on the same terms with each other then as they are now. The final results had Labour on 50 seats, Progressives with 1 seat and the Green Party with 6 seats, for a total of 57 seats – not enough to govern without the additional support of New Zealand First’s 7 seats. Of course that is not how the coalition negotiations worked out, but again that is due to looking at the 2005 results through the lens of the relationships between the parties as they are in 2009, and not a problem with the simulation itself. The ability of the simulation to correctly retrodict the overall outcomes of the 2005 and 2008 NZ General elections gives some confidence in the models it uses.

Finally, we can take the probabilities of the three major scenarios – National-led government, Labour-led government, and Maori Party balance of power – and plot them as a time series graph to show how the probabilities for each scenario have changed over the last 4 or so years. The results are shown in the figure below:

Time series for Scenario Analysis results.

Time series for Scenario Analysis results. Horizontal axis represents the date, starting 60 days before the 2005 NZ General Election, and finishing 60 days from the present. Lines show probabilities of a National-led government (blue), Labour-led government (red) and Maori Party balance of power (pink).

As you can see, Labour’s chances of holding together a winning coalition vanished rapidly within a few months of the 2005 election. The Maori Party were then predicted to hold the balance of power for most of the next two years, before National’s rise in the polls. Other than a brief and small (~5%) dip around the 2008 election, the National Party have looked certain of leading the government since about late November 2007. Ignore the small dip in National’s probability on the far right of the graph, that merely reflects the uncertainty due the errors on the polling averages blowing up because the simulation is performed too far in the future. They may vanish depending on future polling.

Due to National’s current lead in polling these graphs are unlikely to change significantly in the near future, so I won’t be writing too many front page posts on them. I will try to make the most recent Scenario Analysis graphs available on the graphs page though, so please have a look there if interested whenever new polls come out.

Read Full Post »