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HomeHealth EconomicsA Bayesian evaluation of polls within the Catalan elections

A Bayesian evaluation of polls within the Catalan elections

(Invited put up by Virgilio Gómez-Rubio, UCLM, Albacete, Spain. Thanks Gianluca for the invitation!!)

I’ve been concerned within the planning and evaluation or survey polls virtually since I got here again to Albacete 9 years in the past. Final months in Spanish politics have been dominated by the ‘Catalan referendum’ and the decision for brand spanking new elections from the nationwide authorities by way of article 155 within the Spanish Structure (which had by no means been enforced earlier than). This elections have been completely different for a lot of causes, so I made a decision to do a (final minute) evaluation of the accessible polls to attempt to predict the allocation of seats within the elections.

The Catalan parliament has 135 seats, cut up in 4 electoral districts which correspond to the 4 provinces within the area, with completely different variety of seats relying on their inhabitants: Barcelona (85 seats), Gerona (17 seats), Lérida (15 seats) and Tarragona (18 seats). Seats are allotted in line with D’Hondt methodology.

A number of polls have been printed within the mass media, and the proportions of votes to events (in addition to pattern dimension, and so forth.)  are both reported on the regional stage  (which is ineffective to allocate seats per provinces) and province stage. Given that the majority polls are aggregated on the regional stage it is smart to mix each kinds of polls right into a single mannequin to supply some perception on the voters’ preferences on the province stage to allocate the variety of seats.

Bayesian hierarchical fashions are nice at combining info from completely different sources. The mannequin that I’ve thought-about now may be very easy. The variety of votes (reported within the ballot) to every celebration on the regional stage are assumed to observe a multinomial distribution with possibilities $P_i,  i=1,ldots, p$, the place $p$ is the variety of political events. On this case, we’ve got 7 essential events plus one other group for ‘different events’. Possibilities $P_i$ are assigned a imprecise Dirichlet prior. The variety of votes on the province stage are assumed to observe a multinomial distribution as nicely, with possibilities $p_{i,j}, i=1,ldots,p, j=1,ldots,4.$. Each possibilities are linked by assuming that $log(p_{i,j})$ is proportional to  $log(P_i)$ plus a province-party particular random impact $u_{i,j}$. I’ve used this mannequin earlier than with good outcomes.

So simple as it’s, this mannequin permits the mix of polls at completely different aggregation ranges. I’ve used JAGS to suit the mannequin and to allocate the variety of seats by exploiting the possibilities from the MCMC output to acquire 10000 attracts of the allocation of seats by making use of D’Hont rule to the proportion of votes to every celebration on the confirmed stage.

Subsequent plot exhibits the distribution of seats in opposition to the precise distribution of seats:

I might say the protection is sweet for many events. Polls didn’t present the lack of voters for CUP and Partido In style (PP).

One other good factor of being Bayesian (and utilizing MCMC) is that different possibilities may very well be computed. For instance, the following plot exhibits the posterior distribution of the variety of seats allotted to pro-independence events in order that the chance of them having a majority may be computed (59.86%):

As I promised to have a shot for every seat allotted appropriately, I’ve received some work left to do till the top of the Christmas break… Merry Christmas and Completely satisfied New 12 months!!!



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