Our statistical model estimates the seats that each party will win and with which probability. It aggregates dozens of polls and historical data to perform 15.000 simulations of the electoral results. Spanish law does not allow polls to be spread after December 14th, so we only consider those published before.

The following graph shows the total seats for each party.

PP would win between 109 and 131 deputies. PSOE would get around 80 deputies, Ciudadanos between 56 and 71, and Podemos, between 44 and 63. Seven other parties would also get seats.

The following table summarizes these results.

The predictions are relatively uncertain. Podemos can easily get 63 seats, or even go higher than 76 seats. PSOE could win less than 69 seats or Ciudadanos could get no more than 56 —as it happens in one out of four simulations—. This uncertainty has two sources: the intrinsic error of public polls and last-week changes on public opinion. Since December 11th, for example, our model estimates that PSOE has lost 2 seats and Ciudadanos 6, while Podemos won 8.

This uncertainty implies that parties could change their relative positions. All three —PSOE, Ciudadanos and Podemos— may still be second, third or fourth.

WHO CAN FORM A COALITION TO ELECT THE PRESIDENT?

Several parties will need to reach an agreement in order to elect the next president. Our simulation model calculates which coalitions are (arithmetically) possible. We have calculated the likelyhood that different combinations of parties will reach the 176 seats that make up the majority.

PP and Ciudadanos have a 66% chance of reaching a majority of seats. The most likely alternative is a coalition of three to replace Mariano Rajoy: PSOE, Ciudadanos and Podemos have a 91% chance of reaching the necessary number of deputies.

Other coalitions are less likely: PSOE and Ciudadanos only make 176 deputies in 2% of all simulations. A left coalition has a 7% or 8% chance of getting a majority. The 'gran coalición' between PP and PSOE would probably get 176 seats, but this result is politically unlikely.

THE NUMBER OF DEPUTIES IN EACH DISTRICT

The following table shows the seats that each party would get in each district. The "likely seats" (those with more than a 75% chance) are represented in a darker color. The "possible seats" are represented in a lighter color: "Possible seats" have a 50% chance, between 25% and 75%.

WHAT CAN HAPPEN BEFORE ELECTION DAY?

Voters change their minds. We have being monitoring their evolution with our 'poll of polls' —it includes dozens of polls weighted by date, sample size and house effects-. We can even try to make a forecast based on those trends, but this is a risky exercise.

On Monday the polls showed two trends: Ciudadanos was recessing and Podemos was gaining votes. Those trajectories could continue, stop or even revert. But if one assumes that they have continued, our predictions will change.

We can simulate an hypothetical scenario where the vote shares of Podemos and Ciudadanos exchanged: Ciudadanos will have a 17,5% vote share and Podemos a 19%. In this scenario our model prediction will be the following:

Podemos would get around 62 seats and Ciudadanos around 58. That is, Podemos will (probably) get more seats than Ciudadanos, but not in proportion to its votes. This happens because of the territorial distribution of the two parties voters: Ciudadanos has an advantage because they get more votes in small districts, and there the Spanish electoral system makes seats 'cheaper' in votes.

In this scenario Podemos has a 39% chance of being fourth, a 42% of being third, and a 17% of being second. Ciudadanos has chances 50%, 37% and 10%, respectivelly. PSOE will be second with a 70% chance.

The chance of different coalitions will also change in this hypothetical scenario. PP and Ciudadanos will have only a 50% chance of reaching a majority of seats. A left coalition will have a 15% chance, so is still unlikely. A coalition of three with PSOE, Ciudadanos and Podemos will have a 92% chance.

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The results of the next Spanish election are highly uncertain for several reasons. Many voters are undecided, coalitions are unclear, and we have no historical records for the new parties. And besides all this we have volatility: during this last weeks polls –and probably voters– have changed a lot.

Note: Podemos results include seats won by Podemos’ coalitions with other parties in Cataluña, Comunidad Valenciana and Galicia. The coalition in Galicia also includes IU.

Methodology

Our model estimates the seats in each district. It uses dozens of polls and historical results to perform 15.000 simulations of the 20D elections. This way it estimates the seats that each party will win and with which probability.

The model follows a four-step procedure.

Step 1. Calculate a weigthed average of national polls. These polls are provided by Metroscopia, My Word, Celestetel, Sigma Dos, Invymark, Simple Lógica, NC Report, Encuestamos, Demoscopia Servicios, DYM, GESOP, GETS, TNS Demoscopia y el CIS.

Step 2. Approximate the votes shares in each district. We use historical data and polls to do this. This distribution is perfomed in a way that guarantees that the total votes are those estimated by the weigthed average of polls at a national level.

Step 3. Incorporate uncertainty into the model. We have calibrated the degree of uncertainty by evaluating the results of polls in seven elections of the last five years.

Step 4. Simulate: The last step is to run the model to perform 15.000 simulations of electoral results at each district. The we compute agregates, majorities, etc.

You can read more details about the methodology here (Spanish).