Introduction

• General elections can generate substantial shifts in economic outcomes.
• Predicting election outcomes thus very important.
  • Additionally, impact of expectations on economic outcomes of interest.
• Election tomorrow arguably the most uncertain for a generation:
  • Who will win most seats?
  • What coalitions will have sufficient seats to govern?
• This election may be the single most forecast election in UK history.
• Purpose of today’s talk:
  • Set out a range of different forecasts using different information.

General Election

• How can we predict the election outcome?
• Many are already doing so:
  • http://www.electionforecast.co.uk/ (and FiveThirtyEight):
    • CON 281, LAB 266, SNP 52, LIB 26, UKIP 1.
  • http://www.ukelect.co.uk/HTML/forecasts.html
    • CON 271, LAB 272, SNP 55, LIB 27, UKIP 2.
  • http://www.electoralcalculus.co.uk/homepage.html
    • CON 282, LAB 275, SNP 52, LIB 18, UKIP 1.
  • http://may2015.com/category/seat-calculator/:
    • CON 273, LAB 268, SNP 56, LIB 28, UKIP 2.
  • http://www.theguardian.com/politics/ng-interactive/2015/feb/27/guardian-poll-projection:
    • CON 276, LAB 269, SNP 53, LIB 27, UKIP 3.
  • http://ntuelectionexperts2015.com/2015/05/05/tories-ahead-with-two-days-to-go-uk-election-forecast-5-may-2015/:
    • CON 283, LAB 267, SNP 49, LIB 25, UKIP 3.
• Any forecast is some function of the information available:
  • Opinion polls, constituency and national level.
  • Bookmaker prices.
  • Economic fundamentals.
  • Social media?
• Huge number of sources of information:
  • How can we transform this information into seats? Can we?
  • All forecasts some function of available information.

What research guides us?

• Numerous studies of opinion polls, mainly US based:
  • E.g.: Gelman and King (1993)
• Some studies comparing opinion polls and prediction markets:
  • E.g.: Chen et al. (2005), Leigh and Wolfers (2006), Kou and Sobel (2004), Vaughan Williams and Reade (2014)
• Some studies looking comparing even more widely:
  • Vaughan Williams and Reade (2015)
• Most of these studies are US-focussed.
  • Any obvious reason why polls vs bookies/markets vs experts would be different in UK?

Source of Information

• Opinion polls?
  • Outcome determined by seats, not vote shares.
  • Historical data on seats?
• Constituency polls?
  • Different patterns in different parts of the country.
  • Lord Ashcroft publishing unprecedented number of constituency polls.
  • Problem: How do constituency outcomes relate to prior opinion polling?
    • Only historical guide is by-elections since 2010.
  • Resource: http://en.wikipedia.org/wiki/Opinion_polling_in_United_Kingdom_constituencies,_2010%E2%80%9315
• Fundamentals?
  • Do vote shares depend on the economic situation?
• Bookmakers?
  • Provide forecasts on wide range of events.
  • Including every seat, banded seats, etc.

National Opinion Polls to Seats?

• Do national opinion polls contain useful information for seats?

• We can create a linear regression model on historical data: \[ seats_{it} = \beta_0 + \beta_1 X_{it} + e_{it}. \]
• Here:
  • \(seats_{it}\) is seats for party \(i\) at election \(t\).
  • \(X_{it}\) is a set of explanatory variables for party \(i\) at election \(t\). Includes:
    • Opinion poll vote share.

    • Days between poll and election.

      Estimate	Std. Error	t value P	r(>|t|)
      (Intercept)	-114.865	10.335	-11.115	0.000
      Poll.Share	10.029	0.276	36.272	0.000
      partyLAB	85.159	10.863	7.839	0.000
      partyLIB	150.796	11.289	13.358	0.000
      days.until	0.127	0.013	9.798	0.000
      incumbent	116.073	10.532	11.021	0.000
      Poll.Share:partyLAB	-2.369	0.285	-8.298	0.000
      Poll.Share:partyLIB	-9.941	0.364	-27.286	0.000
      Poll.Share:days.until	-0.003	0.000	-8.254	0.000
      partyLAB:days.until	-0.021	0.014	-1.482	0.138
      partyLIB:days.until	-0.142	0.014	-10.067	0.000
      Poll.Share:incumbent	-1.284	0.275	-4.660	0.000
      days.until:incumbent	-0.088	0.014	-6.284	0.000
      Poll.Share:partyLAB:days.until	0.000	0.000	1.312	0.190
      Poll.Share:partyLIB:days.until	0.004	0.000	8.166	0.000
      Poll.Share:days.until:incumbent	0.001	0.000	3.192	0.001

• Plot is actual seats against polled vote shares, and predicted seats against polled vote shares.

• Now we can look at how we’d have forecast 2010:

• Now we can look at 2015’s forecasts:

Simulation-based Forecasting

• General elections remain data-rich environment.
  • 650 seat outcomes, 4–5 candidates, every 4/5 years.
• Interest in changes between elections:
  • How much does vote share vary, on average?
  • Is it enough to affect outcomes?
• Most forecasts are point forecasts:
  • LAB 267, CON 276, etc.
  • Little concept of uncertainty surrounding forecasts.
• Proposal: Draw changes in party vote in constituencies at random from historical distribution:
  • Repeat process sufficiently often to generate probability distribution of likely outcomes.
• Data on constituency outcomes back to 1983 from http://www.electoralcalculus.co.uk:
  • Back much further from 1936 from <>.

Simulation-based Forecasts I

• Method:
  • Draw swing from distribution of swings for each party in each seat.
  • Sum up total seat outcomes, store, repeat process.

• As would be expected, variation only around 2010 result.
  • Nonetheless, highlights potential for method.
  • Can attach probabilities to outcomes.

Simulation-based Forecasts II: Variations

• Variations:
  • Adjust for incumbency effect?
  • Adjust for national polling?
  • Adjust for constituency polling?
  • Adjust for bookmaker odds?
• Incumbency effect seemingly favours Labour too much.
• Constituency polling enables recognition of likely role Nationalists will play.

• Even with most recent constituency polls, LAB largest party 76.4% of time.
  • Contrasts with essentially all published forecasts.
  • But: What do we judge forecasts against?

Forecasting the General Election: Bookmakers

• Research suggests bookmakers reasonable forecasts:
  • Vaughan Williams and Reade (2015), Vaughan Williams and Reade (2014).
• Caveat regarding favourite-longshot bias:
  • But we found surprisingly little evidence of this in US elections.
• Implied probabilities.
  • With traditional odds (3-to-1 etc), we can turn them into implied probabilities.
  • Treat traditional odds as fraction, so 3-to-1 is 3, but 3-to-1 on is 1/3.
  • Add 1 to the traditional odds fractionised, this gives decimal odds.
  • Take reciprocal of decimal odds to get implied probability.

• Majorities, fine, but what about seats?

• Who is expected to win the most?
  • To look at this question, we can look at bookmaker odds for the most seats.
  • Bookmakers offer bets on who will win most seats.

• But who will be PM?

More Simulation: Bookmaker Implied Forecasts

• Can apply simulation method to bookmaker forecasts:
  • http://www.oddsportal.com reports betting prices for each constituency.
  • Seventeen bookmakers have provided prices across 640 constituencies.

• But overall outcome probabilistic, simple sums of seats ignores uncertainty.
• Apply simulation method:
  • Draw seat winner according to bookmaker probabilities in each constituency.
    • If no prices, assume 99% chance incumbent holds.
  • Sum up seat totals, record them.
  • Repeat process many times to generate probability distribution.
• http://www.firstpastthepost.net/ reports outcomes constituency betting markets imply.
  • Although does not report uncertainty, nor differences between bookmakers.

Outcomes

Distributions?

Particular Events by Bookies

Conclusions?

• Perhaps the most uncertain yet most forecast election in decades.
• All forecasts different functions of different subsets of vast information set:
  • Can this explain variation in implied forecasts?