This website shows the results of a Monte Carlo simulation of the Australian Senate under the voting rule changes that are currently under consideration.

If you want to examine the results, you can use the following links:

Half Senate Election (ordinary election)

Full Senate Election (double-dissolution election)

This investigation is a statistical analysis of probable election outcomes. A full report on the investigation is available at right. The most important findings are:

  • The average election outcome, as well as the most common outcome, was a Senate controlled by Labor and The Greens.
  • It is practically impossible for the Liberal/National Coalition to gain control of the Senate using the changed rules, whether there is a double-dissolution election or not.
  • The Coalition would in fact gain a majority in the Senate at only one out of 400 double-dissolution elections, given current voting patterns.
  • The Greens stand to gain the most as they will become a permanent cross-bench, and will almost always be the only party that the Coalition or Labor can negotiate with to pass legislation (other than each other).

The simulation undertaken is known as a Monte-Carlo simulation, which simulates many randomly generated, likely voting patterns in order to determine the average outcomes. To generate this Monte-Carlo simulation, the means and standard deviations of all significant parties in each state in the last 3 elections were used, as well as a national-level measure of left-right variance (to simulate national left-right swings). These statistics were then used to generate 20,000 likely election results.

The results are rigorous and account for all statistically plausible election swings.

This investigation and analysis has been undertaken by Jebediah Cole (B. Sc./Arts, UNSW), a consultant data analyst and programmer.

Queries: jcole@jcole.id.au

Investigation of proposed Senate changes: full report



A Monte-Carlo simulation was run to generate a set of 20,000 likely election results that were then analysed to investigate the likely senate seat outcomes based on the proposed voting changes.

The proposed Senate voting changes could have a significant political impact on the future composition of the Senate. Analysis so far has focused on re-calculation of historical Senate election results. These analyses have mostly found that the changes would benefit The Greens at the expense of the minor parties, although one researcher used a different method for calculating preference flow that purported to show an advantage for the Coalition in the proposed changes.

The key factor in analysing the likely outcomes of different election methods, is that we do not actually know what the vote will be in the future. Analysis of a limited number of historical elections does not provide a robust picture of likely outcomes in an electoral system like the Senate, where a small change in votes for one party can have a significant impact on outcomes for that party and others.

The Monte-Carlo simulation addresses this challenge by generating an extremely large set of data based on probabilities. This large data set can then be analysed to find robust averages and modes (most common outcomes) that indicate the likely outcomes in a hypothetical system.

To investigate the likely effects of the proposed voting reforms, a large set of electoral data was generated using a Monte-Carlo simulation. This electoral data was in the form of 20,000 independent “elections” that represented the votes for each party in each state. Actual senate seat results were then calculated from these “elections” in the analysis.

Method & Assumptions


The last three federal elections were taken to represent the federal senate voting trends. Only group votes were analysed. Very small parties with no seats in the Senate and parties that have ceased to exist were excluded from the analysis. Parties were placed into right-wing, left-wing, and independent groupings for the purpose of computing national left-right swings. National left-right swings were applied as well as state-by-state, per party variances. It was assumed voting patterns follow normal distributions. Data was randomly generated within these bounds and then analysed en masse for average and most common outcomes.

Input Data Set

The last three federal elections (2013, 2010 & 2007)were used to generate the data. The last three elections were chosen for a number of reasons. Firstly, three elections provides a large enough data set to compute means and standard deviations. Secondly, these three elections are balanced in terms of swings: one election (2007) showed a strong swing to Labor, one election (2010) was very close and one showed a strong swing to the Coalition (2010). Thirdly, going back more than three elections is more than a decade in the past, and voting trends change over time. Historical data, once you go back beyond the current voting fashion era, begins to degrade the quality of analysis.

The original count of the 2013 WA Senate was used, as this data, although it was not used to compose the Senate we have today (there was a re-election in 2014), was nonetheless in step with the election-day swing of the other data, and represents the voting intentions of the WA electorate on that day well enough for our purposes (even if a very small number of votes went missing for the recount).

Not every single vote in these data sets was included in the input data set. To facilitate importation of the data, group votes only were analysed, as non-group votes are very difficult to aggregate and analyse, are statistically a small proportion of the votes, tend to follow similar patterns to the group votes, and very rarely have an effect on the overall outcome.

Some parties were also not included in the analysis. Parties were included in the analysis if:

  • They had polled over 1% nationally in any of the three elections
  • They had polled over an average of 0.5% across those of the three elections they did contest
  • They currently held any seats in the Federal Senate

Parties were excluded if they no longer existed.

The decision was made to treat the One Nation and Pauline parties as one party for this analysis, as even though the parties are controlled by different personalities, the party brand is relatively similar.

Party Groupings

In addition to computing vote variations within the various states, a measure of variance was also added to model national left-right swings. To this end, all the parties included in the analysis were grouped into three broad groups: Broad Left, Broad Right, Independents.

The assumption behind these groupings is that national voting trends oscillate between the left and right and modelling this phenomenon will help to capture Senate results that are characterised by a strong swing from one side of politics to the other.

The Broad Right group includes, Conservatives, Christians, nationalists and libertarians, whilst the Broad Left group includes all of the parties associated with the left wing. Some parties do not fit in either group and made up the much smaller group of Independents.

Broad Right

  • Liberal/National Coalition
  • Palmer United Party
  • Liberal Democratic Party
  • Family First Party
  • Katters Australia Party
  • Christian Democratic Party
  • One Nation / Pauline

Broad Left

  • Australian Labor Party
  • Australian Greens
  • Sex Party
  • HEMP
  • Animal Justice
  • Wikileaks


  • Xenophon Group
  • Democratic Labour Party
  • Australian Motoring Enthusiast Party

Statistical Assumptions

It was assumed that the mean vote of each party in each state at the three elections represented their true mean vote. It was assumed that public voting preferences will follow a “normal distribution” in the future – the programming library used to generate the simulated election outcomes was Rubystats::NormalDistribution.

A random variation conforming to a normal distribution was first applied to the federal level groups according to their standard deviation. This value was then used to adjust the means of each party in each state before the state-wide random variation was applied. In this way, the model accounts for greater nation-wide variation than the historical data sets it was based on. It does this in order to account for stronger national swings than this limited data set contained – the simulation errs on the side of greater variance to capture a wider range of possible outcomes.

It was assumed under the new Senate rules that no preferences would flow from one party to another – ie, that all or almost all votes will continue to be a 1 above the line for a “party group”.


The historical data was imported and saved. This data was then used to compute means and standard deviations for each of the federal-level party groups and the state level parties.

Once these random variations were applied to the means of each party in each state, in the manner described above, the percentages for each party in each state were saved as an “election”. 20,000 elections were simulated and saved as a data set.

The elections were then “calculated” according to the election method for the Senate with no preference flow.

Once the outcomes of the 20,000 elections were calculated, they were then aggregated together and analysed. A total tally of all the seats won by all of the parties was generated to observe the relative electoral success of each party under the system. The modal, or most common, outcome was also isolated to show the general character of an election under the system. Individual histograms of number of seats achieved vs frequency were generated for each party federally and in each state.



Both the average outcome, as well as the most common outcome, was a Senate controlled by Labor and the Greens. To gain control of the Senate, the Liberal/National Coalition require 23 seats from their current position if an ordinary (half) Senate election is held. This did not once occur in 20,000 simulations. Additionally, the Coalition gained the 22 seats required to deadlock the Senate in only 0.06% of cases. Those Coalition supporters pinning their hopes on a full Senate election will also be disappointed: a majority Coalition senate occurred in only 0.26% of cases. Because numbers this small are sometimes confused, I will emphasise that these numbers are fractions of 1%: The Coalition would gain a majority in the Senate once in roughly every 400 double dissolution elections. A Coalition majority after the next election is, in practical terms, impossible, whether or not it is a double-dissolution.

The most common outcome of a full Senate election (ie via a double-dissolution) is that Labor and the Greens gain exactly half of the Senate, and can thereby block legislation.

What this shows is that the Coalition will always be a minority in the Senate. Given the significant reduction in the two party primary votes over the last 30 years, this is inevitable: it is very difficult to engineer an electoral system where an average primary vote of 37.95% yields a majority of Senators.

Labor, on the other hand, are set to gain significantly (on the face of it) from the changes. They are very likely under the new system to get 15-17 Senators in each half Senate election, equating to a typical Senate holding of 32 seats, much more than their existing number (25).

The Greens will gain stability: the changes will give them a typical senate holding of 8-10 Senators, with less than 7 being very uncommon. Although they are unlikely to increase their current holding under the changes, they will entrench their position as a permanent (and as seen below, more important) fixture in Australian politics.

From a game-theory perspective, this change damages the Coalition significantly, and benefits the Greens. Each party that could, in combination with the government, make up a majority of the Senate, is a potential negotiating partner. The more potential negotiating partners there are, the less power each one has when negotiating with the Government. Looking at the ideology of the likely minor parties, which, purely because of the current political landscape, tend to be either nationalist, libertarian or single issue – these are much better negotiating partners for a Coalition government than two left-wing parties.

By reducing the number of potential negotiating partners down to these two, one of whom is the primary opposition party, the Coalition will massively reduce their ability to pass legislation through the Senate when they are in government, and significantly increase the effective power of the Greens. Applying the same analysis, The Greens will, in fact, enjoy increased power during Labor governments as well – which could be the real cause of Labor’s decision to reverse course and oppose the proposed voting changes.