### A Totally Gay Math Problem

In the wake of Maine rejecting same-sex marriage, here’s a math problem for you:

Given a 53% to 47% split, and the fact that, statistically speaking, the older you are, the more likely you are to be bigoted*, how long will it take before same-sex marriage remains legal (or, at least, is popularly supported**) in Maine?

You are given the following statistics:

• Annual birth rate: 1.16% (this varies, but assume that the population grows by this value each year)
• Annual death rate: 0.93% (source: Maine Vital Statistics)
• In Maine, the portion of the population that supports gay marriage by age:
• 18-29: 69%
• 30-44: 55%
• 45-64: 47%
• 65+: 30% (source: Columbia University. You can assume these rates remain constant, even though they are likely to increase as the population ages)
• Distribution of deaths within the same age groups:
• 18-29: 2% (extrapolated — data provided only in 5-year ranges)
• 30-44: 4%
• 45-64: 19%
• 65+: 73% (source: CDC; I did the summation myself. These values are for the whole country, and are more recent than the birth and death rates for Maine, but for the purposes of this problem, assume Maine has a similar rate.)

Update: It has been pointed out that I have neglected to provide the current population distribution. Sorry, you’re right! I was trying too hard to make a point, and wasn’t being careful enough to provide sufficient information. I’m a little ashamed. Here:

• Assume this current population distribution, by age range:
• 18-29: 21%
• 30-44: 21%
• 45-64: 21% (Unfortunately, I couldn’t find any source for this that gave finer granularity than “19-64″, so these are a rough estimate at best, but I think they should be good enough for our purposes. Let me know if you find something better.)
• 65+: 16% (source: statehealthfacts.org)

In which year will more than 50% of Maine’s population support same-sex marriage? Show your work!

*Bigoted, for the purposes of this problem, means “not in support of same-sex marriage”. You may disagree with this definition, but you’d be wrong. Sorry. I realize that much of my own family falls under that umbrella. This seems to indicate that otherwise decent people can still be bigoted.

**Strictly speaking, this sort of thing shouldn’t be determined by a vote anyway. See the Tyranny of the Majority.

Update 2: This post has been making the rounds, and a common theme among comments seems to be that there are many more factors that influence this: changing age distribution due to people retiring to Maine/younger people leaving, increasing conservatism with age, higher voting rates among the elderly, etc. All of this is true, but it doesn’t matter.

The point is not really to predict the exact date when gay marriage will be popularly supported. It’s that the date, whenever it comes, is inevitable. In the meantime, all I can do is remind us all that the times, once again, are changing. As a straight man, it baffles me that so many people feel so threatened by this. I will not change my mind as I grow older, and I believe enough of my contemporaries feel the same way to feel comfortable making this claim.

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1. Rachel Titley November 5th, 2009 8:29 pm

I will not attempt maths at half 1 in the morning, I will not…
Don’t ask me how I worked it out, and it’s only an approximate, but I got 8 years.
Like I said, half 1 in the morning.

2. Hey November 5th, 2009 8:52 pm

You forgot to show the current proportional split of the current population by age.

3. Adam November 5th, 2009 11:10 pm

Well, if we use the current population estimate as a starting point. (1,316,456 Wikipedia)

Lets assume:
.0116 – .0093 = 0.01067
Year 0 is 2008.

y-hat = 1316456 + .01067x
y-hat ~ 14047 new people per year.

Births: 15270.9
Deaths: 12200.0
Total: 3070 New Births.

Of those deaths we can assume that these are the percent that die.

18-29: 244
30-44: 488
45-64: 2318
65+: 8906

Only 731,591 of the population are voters (2008 election, Wikipedia).

If the vote is split 53% to 47% then these are the amounts.

Against: 387743
For: 343848

Of which:
Against:
45-64: (53%) or 205504
65+: (70%) or 271420

Remember that we lose [2318, 8906] ever year, so. If we sum the votes against against the amount that have died.

Year
1 – 11224/387743 or 2.895%
2 – 22448/387743 or 5.789%
3 – 44896/387743 or 11.578%
4 – 89792/387743 or 23.156%

Against: 297953/754039 = 39.51%
For: 433638/754039 = 57.51%

Does that really show that after two years they will lose 5.7% || 11% of the vote? No, but it can hint that by the next election Maine should have enough to at least tie.

This also assumes that every new voter will vote for same-sex marriage. You also assume that the older folk “drop like flies” (Note, I didn’t factor in the amount of 18-45 lost, it’s fairly low.).

This is only an assumption, but I would expect that in 3-5 years the vote could come back and have a very good chance at allowing same-sex marriage.

4. Eric November 6th, 2009 12:14 am

Sadly, I don’t know statistics. I think it would be a more compelling picture if turnout ratio was factored in there, too, though.

5. [...] software engineer and blogger Frank Pape breaks down all the necessary information to compute the question, which hinges on old people being more conservative, and young people being [...]

6. Greg November 6th, 2009 9:35 am

You have to figure the older people are FAR more likely to turn out and vote than the younger segment. You also have to fine tune the population distribution to account for the fact that the baby boomers are a significant bulge of population (age 45 to 65 I believe). And, in California, babyboomers were less than 50% likely to support gay marriage.

7. --bill November 6th, 2009 10:48 am

You leave out immigration, both into and out of the state. From 1990-2000, the percent of Maine’s population aged 0-34 dropped by 8 percent; the percentage aged 34-85+ increased by 10 percent. See
ElderWeb . People retire to Maine, while young people move out.

8. W.W.WTF – 11/06 « Skeptigay November 6th, 2009 1:39 pm

[...] – 11/06 By skeptigay http://www.distracto.net/2009/11/a-totally-gay-math-problem/ - Gay AND Math, together-like some kind of blastphemous marriage. Gotta love [...]

9. The Cali Garmo November 7th, 2009 11:36 am

This concept is actually fairly easily seen in California too! Luckily we have had 2 votes on marriage equality and so it’s much simpler to make a (VERY) vague description of when marriage equality will come to the state.

Considering that in 2000 Prop 22 banning same-sex marriage passed with 61.4%
And considering that in 2008 Prop 8 banning same-sex marriage passed with 52.5%

It seems that in 8 years there was a 9% drop in hatred toward same-sex marriage. This roughly translates to that in 2010 CA will have close to a dead split with the opposers slightly ahead and in 2012 having the opposers be in the minority for the first time.

My number 3 years seems fairly close to @Adam ‘s 3-5 years for Maine where maine is currently at 53% which suggests taking a little longer than CA.

But again, these are EXTREMELY rough estimates and don’t actually signify any trend. After all, if you give me any 2 points I can create you any line you so desire hitting any points you wish.