What is wrong with my method for predicting the election?

[SlurrerOfSpeech]

Given the fact that there are 51 states and districts, there are 2⁵¹ subcollections of the 51 states, which I can't possibly iterate over entirely. So what I do is find 2¹⁰ subcollections of states whose electoral votes summed are 270 or greater. I then sum together the probabilities of Trump winning each of those 2¹⁰ collection of states. Finally, I multiply that sum by 2⁴¹.

Anything wrong with that? Because I'm getting a results that seems wrong.

 

[QuantumQuest]

You're extrapolating a small sample - comparing to ($2^{51}$), by a huge number ($2^{41}$) so the result is way off.

 

[SlurrerOfSpeech]

Can you help me figure out why this is always calculating to ~0.99? It should be calculating to ~0.50 since I put an equal chance of an R or D winning.

const VOTES_TO_WIN = 270;

// State name, number of electoral votes, and Republican and
// Democrat nominee polling percent average taken from
// RealClearPolitics.com, rounded to nearest integer
const dataByState = {
    'Washington' : { ElectoralVotes : 12, RChance: 50, DChance: 50 },
    'Oregon': { ElectoralVotes: 7, RChance: 50, DChance: 50 },
    'California': { ElectoralVotes: 55, RChance: 50, DChance: 50 },
    'Idaho' : { ElectoralVotes: 4, RChance : 50, DChance: 50 },
    'Nevada' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Montana' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'Wyoming' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'Colorado' : { ElectoralVotes: 9, RChance : 50, DChance: 50 },
    'New Mexico' : { ElectoralVotes: 5, RChance : 50, DChance: 50 },
    'Utah' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Arizona' : { ElectoralVotes: 11, RChance : 50, DChance: 50 },
    'North Dakota' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'South Dakota' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'Nebraska' : { ElectoralVotes: 5, RChance : 50, DChance: 50 },
    'Kansas' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Oklahoma' : { ElectoralVotes: 7, RChance : 50, DChance: 50 },
    'Texas' : { ElectoralVotes: 38, RChance : 50, DChance: 50 },
    'Minnesota' : { ElectoralVotes: 10, RChance : 50, DChance: 50 },
    'Iowa' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Missouri' : { ElectoralVotes: 10, RChance : 50, DChance: 50 },
    'Arkansas' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Lousiana' : { ElectoralVotes: 8, RChance : 50, DChance: 50 },
    'Wisconsin' : { ElectoralVotes: 10, RChance : 50, DChance: 50 },
    'Illinois' : { ElectoralVotes: 20, RChance : 50, DChance: 50 },
    'Tennessee' : { ElectoralVotes: 11, RChance : 50, DChance: 50 },
    'Mississippi' : { ElectoralVotes: 6, RChance : 50, DChance: 50 },
    'Alabama' : { ElectoralVotes: 9, RChance : 50, DChance: 50 },
    'Michigan' : { ElectoralVotes: 16, RChance : 50, DChance: 50 },
    'Indiana' : { ElectoralVotes: 11, RChance : 50, DChance: 50 },
    'Kentucky' : { ElectoralVotes: 8, RChance : 50, DChance: 50 },
    'Ohio' : { ElectoralVotes: 18, RChance : 50, DChance: 50 },
    'West Virginia' : { ElectoralVotes: 5, RChance : 50, DChance: 50 },
    'Virginia' : { ElectoralVotes: 13, RChance : 50, DChance: 50 },
    'North Carolina' : { ElectoralVotes: 15, RChance : 50, DChance: 50 },
    'South Carolina' : { ElectoralVotes: 9, RChance : 50, DChance: 50 },
    'Georgia' : { ElectoralVotes: 16, RChance : 50, DChance: 50 },
    'Florida' : { ElectoralVotes: 29, RChance : 50, DChance: 50 },
    'D.C.' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'Maryland' : { ElectoralVotes: 10, RChance : 50, DChance: 50 },
    'Delaware' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'New Jersey' : { ElectoralVotes: 14, RChance : 50, DChance: 50 },
    'Pennsylvania' : { ElectoralVotes: 20, RChance : 50, DChance: 50 },
    'Connectuicut' : { ElectoralVotes: 7, RChance : 50, DChance: 50 },
    'Rhode Island' : { ElectoralVotes: 4, RChance : 50, DChance: 50 },
    'Massachusetts' : { ElectoralVotes: 11, RChance : 50, DChance: 50 },
    'New York' : { ElectoralVotes: 29, RChance : 50, DChance: 50 },
    'Vermont' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'New Hampshire' : { ElectoralVotes: 4, RChance : 50, DChance: 50 },
    'Maine' : { ElectoralVotes: 4, RChance : 50, DChance: 50 },
    'Alaska' : { ElectoralVotes: 3, RChance : 50, DChance: 50 },
    'Hawaii' : { ElectoralVotes: 4, RChance : 50, DChance: 50 }
};

const states = Object.keys(dataByState);

// Helper for using the above map to get a chance of winning
// from a given poll difference
const calcWinChance = (diff) => {
    const conv = pollConversion.find((x) =>
        x.DiffRange[0] <= diff && x.DiffRange[1] >= diff
    );
    return conv && conv.ChanceWin;
}// Helper returns true or false depending on whether a given
// collection of states has enough combined electoral votes
// to win an election
const hasSufficientVotes = (states) => {
    const votes = states.reduce((sum,state) =>
        sum += dataByState[state].ElectoralVotes
    , 0);
    return votes >= VOTES_TO_WIN;
};

// Helper for getting the combination of states corresponding
// to the inputted bit pattern i
const getCombo = (i) => {
    let combo = [];
    for(var j = 0; j < states.length; ++j)
       if((i >> j) & 1)
           combo.push(states[j]);  
    return combo;      
}

// To be filled out, combos will be a map of a bit pattern
// to the corresponding array of state names
let combos = {};

// Set time limit on
const now = new Date();
const timeout = now.setSeconds(now.getSeconds() + 1); // 1 seconds

// Run simulation
const rangetop = Math.pow(2,states.length) + 1;
while(new Date() < timeout)
{
    const rand = Math.floor(Math.random() * rangetop); 
    if(!combos.hasOwnProperty(rand))
        combos[rand] = getCombo(rand);
}

// Sum up the probabilites of the R candidate winning each
// combination of states that add up to a succifient number
// of electoral votes
let RSum = 0;
const keynums = Object.keys(combos);
console.log("num combos = " + keynums.length);//TEST
keynums.forEach((num) => {
  
    const comboStates = combos[num];
  
    // state combo not counted if it doesn't add up
    // to enough electoral votes
    if(!hasSufficientVotes(comboStates))
        return;
  
    // mutltipy together the probabilities of the R
    // winning the state combo
    let RProb = 1;
    comboStates.forEach((state) => {
        RProb *= dataByState[state].RChance / 100;
    });
    const otherStates = states.filter((state) => !comboStates.includes(state));
    otherStates.forEach((state) => {
        RProb *= dataByState[state].DChance / 100; 
    });

    RSum += RProb;
});

const multiplier = Math.pow(2, states.length + 1) / keynums.length;
RSum *= multiplier;

alert("RSum = " + RSum);

 

[chiro]

Hey SlurrerOfSpeech.

Are you trying to do a probabilistic/statistical estimate?

If so you could look at doing medians or means with a distribution as opposed to iterating over every outcome and use probabilities to gauge whether an outcome for some group/organization will occur.

The issue you should have is controlling the variance and depending on the constraints you have, you can shrink them dramatically if the information exists.

 

[SlurrerOfSpeech]

Hey SlurrerOfSpeech.

Are you trying to do a probabilistic/statistical estimate?

If so you could look at doing medians or means with a distribution as opposed to iterating over every outcome and use probabilities to gauge whether an outcome for some group/organization will occur.

The issue you should have is controlling the variance and depending on the constraints you have, you can shrink them dramatically if the information exists.

I will try this. Thanks. :)