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My question is about how to do weighting in polls using multiple weights. I think it's a pretty standard statistical question, but I can't find a straightforward answer on the Internet, so I am here to ask.

Let's say I'm conducting a political poll for who voters prefer in a coming election between Mickey Mouse and Donald Duck and I have the following raw numbers from a 740-person sample:

{ Mickey Mouse:
  total: 370,
  { gender: {
    male: 110,
    female: 260
  },
  { race: {
    white: 150,
    black: 140,
    hispanic: 70,
    asian: 9,
    other: 1
  }
}

{ Donald Duck:
  total: 370,
  { gender: {
    male: 210,
    female: 160
  },
  { race: {
    white: 170,
    black: 140,
    hispanic: 40,
    asian: 18,
    other: 2
  }
}

Let's also say that my population of expected voters on Election Day is as follows in percentages:

{ "General population":
  { gender: {
    male: 52,
    female: 48
  },
  { race: {
    white: 60,
    black: 25,
    hispanic: 10,
    asian: 4,
    other: 1
  }
}

I know that to weigh one variable (such as gender), I would divide population percentage by sample percentage to get a weight. In my example above, men comprise 320 of the sample population (which is 43%), and so my weighted calculation for male would be 0.43 / 0.52 = 0.83, and each man who voted for either candidate would only be counted as 0.83 of a vote. Women are 58% of my sample, and so the weight for female would be 0.58 / 0.48 = 1.22, and each woman would count as 1.22 of a vote. Am I correct so far?

However, if I wanted to weigh for both gender and race, how can I do so? Do I multiply the weights together? Do I need more granular population data, i.e. for gender and race combined?

I'm looking for someone to help me understand how to do such a calculation. Thank you.

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