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%%%%%%%%%%%%%%%%%%%%%%%%%%% The calculation %%%%%%%%%%%%%%%%%%%%%%%%
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%
% Changes for Senate projection
% make the histogram num_states wide
% use EV variable to give 1 seat per race (keep variable name same)
%
% Calculate z-score and convert to probability, assuming normal distribution.
polls.z=(polls.margin+biaspct)./polls.SEM;
polls.prob_Dem_win=tcdf(polls.z,2); % polls.prob_Dem_win=(erf(polls.z/sqrt(2))+1)/2;
polls.prob_GOP_win=1-polls.prob_Dem_win;
%
polls.znov=(polls.margin+biaspct)./sqrt(polls.SEM.*polls.SEM+5*5);
polls.prob_Dem_November=tcdf(polls.znov,2);
%polls.prob_Dem_November=(erf(polls.znov/sqrt(2))+1)/2;
%
stateprobs=round(polls.prob_Dem_win*100);
statenovprobs=round(polls.prob_Dem_November*100);
% The meta-magic
EV_distribution=[1-polls.prob_Dem_win(1) polls.prob_Dem_win(1)];
for i=2:num_states
nextEV=[1-polls.prob_Dem_win(i) polls.prob_Dem_win(i)];
EV_distribution=conv(EV_distribution,nextEV);
end
clear nextEV
% EV_distribution is the exact probability distribution of
% all 2,251,799,813,685,248 (2.3 quadrillion) possible outcomes. (Wow!)
% 5 July 2014: code is same for Senate. In 2014, 36 races with 11 races in
% question. Therefore 2^11=2048 possibilities.
% Cumulative histogram of all possibilities
histogram=EV_distribution(2:num_states+1); %index of 1 for 1 Dem/Ind seat...num_states for num_states seats
% Truncate distribution by 1, which implicitly assumes at least one race will go to Democrats.
% Seems ok, since otherwise we wouldn't bother doing a simulation.
cumulative_prob=cumsum(histogram);
%
% Calculate properties of distribution using cumulative histogram
% 5 July 2014: All variables below this line are new relative to EV_median.m
%
Senateseats=Demsafe+1:Demsafe+num_states;
R_Senate_control_probability=cumulative_prob(max(49-Demsafe,0));
% if Democrats/Independents get 49 or fewer, Republicans take over
% 49 because VP Biden is a Democrat. will need Demsafe from other script
% 50 in years when VP is a Republican.
D_Senate_control_probability=1-R_Senate_control_probability;
median_seats=Senateseats(min(find(cumulative_prob>=0.5))); % 50% of outcomes
mean_seats=sum(histogram.*Senateseats);
mean_seats=round(mean_seats*100)/100;