```! LINGO model to compute the probability of outcomes in U.S. Presidential Election Electoral College.; ! The overall model consists of two submodels: a) A simple model to convert the fractions of decided voters for each party in a state into a single probability a specified party will get all electoral votes from the state. b) A computationally intense model to compute the overall probability of a specifed party wins, given the probability for each state of a win; ! Keywords: Election, Presidential election, Electoral college, Probability of winning; ! LINGO can be downloaded from http://www.lindo.com ; SETS: STATE: VOTES, PD, POPD, POPR; KNT/1..275/:; KXS( KNT, STATE): WAYS; ENDSETS DATA: ! Computing Vote Probabilities with LINGO; ! Definitions: Inputs: VOTES(j) = electoral votes for state j, POPD(j) = proportion of population definitely voting Democratic, POPR(j) = proportion of population definitely voting Republican UVD = adjustment down of estimated Democratic popularity, to give the assured fraction vote for a candidate. UVR = adjustment down of estimiated Republican popularity, etc.; ! Computed inputs: PD(j) = estimated probability electors for state j vote Democratic.; UVD = 0; UVR = 0; ! Electoral vote counts are for 2012; ! Popularity fractions based loosely on www.electoral-vote.com; STATE, VOTES, POPD, POPR = ! State Votes P(Dem) P(Repb); Alabama 9 0.36 0.54 Alaska 3 0.38 0.59 Arizona 11 0.44 0.52 Arkansas 6 0.30 0.58 California 55 0.56 0.33 Colorado 9 0.45 0.46 Connecticut 7 0.52 0.45 Delaware 3 0.62 0.37 DC 3 0.52 0.48 Florida 29 0.47 0.47 Georgia 16 0.44 0.52 Hawaii 4 0.62 0.30 Idaho 4 0.21 0.64 Illinois 20 0.55 0.36 Indiana 11 0.42 0.55 Iowa 6 0.47 0.42 Kansas 6 0.42 0.57 Kentucky 8 0.39 0.53 Louisiana 8 0.37 0.49 Maryland 10 0.55 0.36 Massachusetts 11 0.64 0.31 Michigan 16 0.48 0.42 Minnesota 10 0.49 0.43 Mississippi 6 0.43 0.56 Missouri 10 0.41 0.54 Montana 3 0.43 0.49 Nevada 6 0.49 0.46 New_Hampshire 4 0.49 0.47 New_Jersey 14 0.51 0.41 New_Mexico 5 0.50 0.41 New_York 29 0.62 0.33 North_Carolina 15 0.45 0.46 North_Dakota 3 0.39 0.54 Ohio 18 0.49 0.49 Oklahoma 7 0.38 0.58 Oregon 7 0.47 0.41 Pennsylvania 20 0.49 0.45 Rhode_Island 4 0.58 0.32 South_Carolina 9 0.40 0.46 South_Dakota 3 0.41 0.52 Tennessee 11 0.34 0.59 Texas 38 0.39 0.55 Utah 6 0.21 0.70 Vermont 3 0.62 0.31 Virginia 13 0.47 0.47 Washington 12 0.50 0.45 West_Virginia 5 0.38 0.52 Wisconsin 10 0.49 0.46 Wyoming 3 0.33 0.64 ! Maine and Nebraska are special in that they can split their votes, so break them up into little states; Maine1 1 0.51 0.37 Maine2 1 0.51 0.37 Maine3 1 0.51 0.37 Maine4 1 0.51 0.37 Nebraska1 1 0.39 0.58 Nebraska2 1 0.39 0.58 Nebraska3 1 0.39 0.58 Nebraska4 1 0.39 0.58 Nebraska5 1 0.39 0.58 ; ENDDATA CALC: @SET( 'TERSEO', 2); ! Turn of default output; ! Submodel (a) to convert popular support for each candidate in a state into a probability the state votes Democratic. This submodel assumes that the outcome of uncertain voters will be uniformly distributed. Suppose for Colorado, the Republican committed fraction is 46% and the Democratic committed fraction is about 45%. Thus, the uncommitted fraction is 9%, then the Republican will win if he gets from 4% to 9% from the uncertain voters. Thus, the model assumes the Republican probability of winning Colorado is 5/9 = 0.555555; @FOR( STATE(J): ! Subtract an uncertainty factor from each popularity fraction; POPDA = @SMAX(0,POPD(J) - UVD); POPRA = @SMAX(0,POPR(J) - UVR); ! Now assume the uncertain part of the population distributes its vote uniformly between the two candidates; @IFC( POPDA + POPRA #LT# 1: PD(J) = @SMIN(1,@SMAX(0,(1-POPRA-0.5)/(1-POPDA-POPRA))); @ELSE PD(J) = POPDA; ); ); ! Submodel (b) to compute overall probability of a win, given a probability for each state of a win, and its number of electoral votes. WAYS( I, J) = Probability a Democrat electoral count of I-1, using only the first J states; ! Before we include any states, there is no way; @FOR( KNT(I): WAYS(I,1) = 0; ); ! Now do the first state; WAYS(1,1) = 1 - PD(1); ! Vote count of 0; WAYS(1+VOTES(1),1) = PD(1); ! Vote count of VOTES(1); ! Now the rest of the states; @FOR( STATE( J) | J #GT# 1: @FOR( KNT( I)| I - VOTES( J) #LE# 0: WAYS( I, J) = WAYS( I, J - 1)*(1 - PD(J)); ); ! We can get to I,J either without this state or with it; @FOR( KNT( I)| I - VOTES( J) #GT# 0: WAYS( I, J) = WAYS( I, J - 1)*(1-PD(J)) + WAYS( I - VOTES( J), J - 1)*PD(J); ); ); ! Write a simple report; @WRITE(@NEWLINE(1),' Probability of various outcomes for U.S. Electoral College.',@NEWLINE(1)); TOTVOTES = @SUM( STATE(J): VOTES(J)); SPLIT = @FLOOR( TOTVOTES/2); NEED = SPLIT + 1; @WRITE( UVD,' = under vote fraction, Democratic',@NEWLINE(1)); @WRITE( UVR,' = under vote fraction, Republican',@NEWLINE(1)); @WRITE( TOTVOTES,' = Number of votes.',@NEWLINE(1)); @WRITE( SPLIT,' = Number of votes needed to tie.',@NEWLINE(1)); @WRITE( NEED,' = Number of votes needed to win.',@NEWLINE(1)); NSTATES = @SIZE(STATE); PDWIN = 1 - @SUM( KNT(I) | I-1 #LT# NEED: WAYS(I,NSTATES)); @WRITE( PDWIN,' = Probability of at least ',NEED,' Democratic votes.',@NEWLINE(1)); @WRITE( WAYS(SPLIT+1,NSTATES),' Probability of exactly ', SPLIT, ' votes.',@NEWLINE(1)); ENDCALC ```