Probability of blue eyes in Canada's PMs

[Hornbein]

Did you get the blues from eating kale? Did you stop eating kale after you realized you would rather be dead? ;-)

I did feel I'd rather be dead than lift weights.

 

[Hornbein]

Go vegetarian and you can wear your shirts unwashed for months and they still smell neutral. It's very convenient. I wonder why this isn't more widely known.

 

[Dale]

It was after I turned vegetarian. But then why did my eyes revert to their original color? A mystery of science.

Were you getting your vegetables from Arrakis that year?

 

[Hornbein]

Were you getting your vegetables from Arrakis that year?

Japanese produce is the greatest. Broccoli lasts for weeks. Another thing I didn't think was possible. Grapes are $40 a bunch but worth it. Just three or so are enough. Restaurants there don't serve produce so you can get a better meal at the supermarket and cook it yourself. Japan is about 80% mountains so farmland is at a great premium. Farmers have little plots and concentrate intently on growing the highest quality they can. This has been going on for centuries so they have it all figured out. Roasted garlic is seldom seen but it's great. Sweet instead of pungent, sticky and black black black. I used to ride a bicycle an hour to get it. The food is so satisfying I lost 15 pounds in a couple of months and didn't even know it. I thought there was something wrong with the scale.

People don't entertain at home so the entertainment districts are enormous. Yokohama's is maybe a square mile. Booze is extremely cheap, hardly taxed at all. Tokyo has maybe a hundred jazz bars and five symphony orchestras. Most forms of music, miles ahead of anywhere else. Painting, same.

I was stuck in Tokyo for two years during Covid on a three month tourist visa. Luckiest thing that ever happened to me. Tokyo is cheap, quiet, and very bicycle friendly. And it got much cheaper after I left. No one believes this. You can rent a microapartment for $150 a month. It's wretched but beats having nothing. The only expensive things are taxicabs and peanuts.

The few homeless people are often very neat and clean. They have shacks with gardens on the floodplain next to the river. I even saw one growing crops under a cell phone tower.

There are abandoned bicycles everywhere. I estimate 30,000 in Tokyo at any time. It's because they are cheap and not allowed on the Metro so if you don't have a car they aren't worthwhile to move. Abandoned autos, vans, and houses are not unusual. Japan is extremely lush, it makes central Bali look sparce. Vines grow on everything that doesn't move, so the abandoned stuff gets covered with those.

J people don't like to be told what to do. I have a collection of photos of bicycles parked directly under No Bicycle Parking signs.

But no one has blue eyes. Except the mind reader from Moldova who was getting a PhD in biochemistry at Todai. But that is another story.

 

[phyzguy]

Of course there are biases. I could just as easily observe that there have been 45 US presidents, all male. The chance of this happening is (1/2)^45 = 2.8E-14. What an amazing coincidence!!

 

[Dale]

Of course there are biases. I could just as easily observe that there have been 45 US presidents, all male. The chance of this happening is (1/2)^45 = 2.8E-14. What an amazing coincidence!!

That is a good example. It shows why non-random samples cannot be assumed to follow the statistics of the underlying population. It is the core reason why polling is difficult and “polling misses” happen.

 

[DaveC426913]

That is a good example. It shows why non-random samples cannot be assumed to follow the statistics of the underlying population. It is the core reason why polling is difficult and “polling misses” happen.

Of course. No one doubts the correlation between gender and presidentness. Extremely gender-biased.

But eye-colour? What's weird is that there seems to be a strong correlation yet no readily available explanation as to why.

The most obvious (if not the most defensible) is the most direct: Canadians just simply prefer blue-eyed people, whether or not they know why.

I doubt this. I doubt Canadians are choosing their leader by eye-colour. But I don't have any theories about any indirect causes that might provide a correlation. It's not like Canadians have an affinity for Aryan politics or anything...


Best guess is that Canada's leadership has been largely drawn from well-educated and wealthy Northern European and British stock, where there is a higher proportion of blue eyes.

https://en.wikipedia.org/wiki/Eye_color




TIL:
Rayleigh Scattering might be at the heart of my sky blue eyes.

"One possible explanation for the difference in appearance between gray and blue eyes is that gray eyes have larger deposits of collagen in the stroma, so that the light that is reflected from the epithelium undergoes Mie scattering (which is not strongly frequency-dependent) rather than Rayleigh scattering (in which shorter wavelengths of light are scattered more). This would be analogous to the change in the color of the sky, from the blue given by the Rayleigh scattering of sunlight by small gas molecules when the sky is clear, to the gray caused by Mie scattering of large water droplets when the sky is cloudy."

 

[Dale]

But eye-colour? What's weird is that there seems to be a strong correlation yet no readily available explanation as to why.

Indeed, the statistics don’t offer any hint about that. All the statistics show is that:

1) the PM population has a significantly higher proportion of blue eyes
2) given that higher proportion, a run of at least 10 in a row is not very unusual

So the puzzle is why are there so many blue eyed PM’s, not why were there 10 in a row. The probabilities that lack explanation are a few in ten to a hundred, not a few in one million to ten million.

The map you showed is already in the right ballpark in terms of the probabilities. PMs tend to be wealthy, and both wealth and eye-color are strongly influenced by family heritage. That probably is a sufficient explanation and could be backed up with statistics on eye color and wealth and political office.

 

[256bits]

Canadians just simply prefer blue-eyed people

We do not know the eye colour of the leader of the loosing team.
If brown, then perhaps there is a preference for blue eyed PMs.
If the opposition leader also has blue eyes, then there is no choice to make on eye colour.

But as you say that is a doubtful proposition.
Considering the flack Harper got over 'those eyes' 'I don't trust him' from those opposed to the Conservative governemnt at the time, it would appear that eye colour blue could just as well have a detrimental effect upon being chosen PM, if anecdotal evidence is to be carried over as representative within certain voters.

 

[256bits]

Canada's leadership has been largely drawn from well-educated and wealthy

I don't know about the wealthy part for all the leaders.
They may leave politics more wealthy than when coming in, but quite a few have come from working families, educated themselves mostly as lawyers it would seem, and made valuable connections through their time spent on education or career.

https://www.noscommunes.ca/procedure-and-practice-4/app07-e.html
Here is a list of the Opposition leaders within the House of Commons since 1873.
The list is longer than 24 due to several factors such fill-ins while the party leader does not have a seat either by loosing it in election ( such as Poilievre ), or change of leader of the party between elections. Some names are thus duplicates such as Andrew Sheer who was Conservative leader 42nd/43rd Parliament, and fill-in for the 45th Parliament.

Note also that several PMs acted also as Official Opposition leader before becoming PM after their party achieved winning an election, or as Official Opposition leader after a loss.

I count 21 out of the 24 PMs( a quick count- I may have missed some ) served also as leader of the opposition 25 times.
----
Cross referencing with post #22
- of the 21 Opposition party leaders who became PM, we are sure 17 had blue eyes
( 4 were indeterminate or dark eyed )
- of the 25 times serving as leader of opposition, at least 34% ( (25-4)/61 ) of the time the Opposition leader had blue eyes.

We can discount fluke regional politics of Quebec NDP Orange Wave Mulclair (3), Bloc Quebecois (4), as well as designated add-in unelected Opposition leaders of the House(14), yielding 61 - 21 = 40 elected Opposition party leaders.
Above becomes:
- at least 53% ( 25-4)/40 of the time the Official Opposition party leader had blue eyes.
-----
Of the 61 items on the list, rthe majority seem to be of British origin, some French and a spattering of names from other ethnic groups ( Ignatieff, Ambrosse, Bergen ).

conclusion
-----------
The leaders of Canada serving as Prime Minister and Official Opposition have a tendency to be one and the same, often with an exchange of role due to an election.
British influence determined leaders, and may still do to some extent from the waning older population that sang O'Canada in the morning before the start of the school day and God Save the Queen at the end.

If anything it appears that Canadians have not chosen to elect a governing party with a blue eyed leader who will thence become PM. It appears instead that the political parties themselves elect their blue eyed leader, each party then presenting their selection of blue eyed to Canadians as being better than the other.

Why the main federal political parties - Liberal or Conservative - .
I guess they, the members, will have to explain.

 

[DaveC426913]

Considering the flack Harper got over 'those eyes' 'I don't trust him' from those opposed to the Conservative governemnt at the time, it would appear that eye colour blue could just as well have a detrimental effect upon being chosen PM, if anecdotal evidence is to be carried over as representative within certain voters.

Heh. That had occurred to me.

Good ol' "Dead eye" Harper.

 

[haruspex]

The difficulty is that the pool to which this result belongs (macrostate?) is undefined.
If we were to look up the eye colours of the last N heads of each of R countries, how likely is it that we would find a case as extreme as this? And that could be, e.g., finding three mutually adjacent countries where the last five all had green eyes.
Go trawling an ocean of data and you will catch some unusual fish.

 

[FactChecker]

The difficulty is that the pool to which this result belongs (macrostate?) is undefined.
If we were to look up the eye colours of the last N heads of each of R countries, how likely is it that we would find a case as extreme as this? And that could be, e.g., finding three mutually adjacent countries where the last five all had green eyes.
Go trawling an ocean of data and you will catch some unusual fish.

That's a good point, but not fully applicable in this case. The OP does not ask "What are the most unusual things in the world?". That would truly be "trawling an ocean". The OP is Canadian and is naturally interested in his leaders, so the scope of a search for oddities is very limited. IMO, within that scope, the result is odd.
That being said, your objection still applies enough to make any conclusions from probability calculations suspect.

 

[haruspex]

That's a good point, but not fully applicable in this case. The OP does not ask "What are the most unusual things in the world?". That would truly be "trawling an ocean". The OP is Canadian and is naturally interested in his leaders, so the scope of a search for oddities is very limited. IMO, within that scope, the result is odd.

We need to know how the OP came across this factoid. Most likely (?) it was originally noticed by someone unknown to the OP and propagated through social media. This means we have to consider what oddities might be turned up by some population of Canadian amateur researchers.
Besides, I am not Canadian, so to me it falls in the same category as an equivalent factoid from anywhere in the world.

 

[FactChecker]

Besides, I am not Canadian, so to me it falls in the same category as an equivalent factoid from anywhere in the world.

I disagree. Any probabilities depend on the "Universe" that was relevant to how it was discovered in/by the OP, not on your situation.

 

[Dale]

That's a good point, but not fully applicable in this case. The OP does not ask "What are the most unusual things in the world?".

IMO, that is precisely the problem. The OP wasn’t asking anything. He found a surprising observation first, and only then asked a question. When that happens the well-considered probability is always much higher than the naive probability.

IMO, within that scope, the result is odd

Maybe, but ~1:10 to ~1:100 odd rather than ~1:1000000 to ~1:10000000 odd, even within that scope.

 

[FactChecker]

Maybe, but ~1:10 to ~1:100 odd rather than ~1:1000000 to ~1:10000000 odd, even within that scope.

I start with the premise that physical appearance is important for political success.
Then consider that I am not demanding a 5-sigma particle physics result.
Finally, I think that your 1:10 number is far too low.
That is why I strongly suspect that Canadians have a bias for blue eyed PMs.

 

[haruspex]

I disagree. Any probabilities depend on the "Universe" that was relevant to how it was discovered in/by the OP, not on your situation.

But what you consider to be that Universe may depend on your situation. You argued that

The OP is Canadian and is naturally interested in his leaders, so the scope of a search for oddities is very limited.

but we don't know who did the search. Certainly the OP would take more notice of a Canadian oddity. Not being Canadian, I would assess it in a broader context… English speaking world? Anywhere that has prime ministers? …

 

[FactChecker]

But what you consider to be that Universe may depend on your situation. You argued that

but we don't know who did the search.

Does that matter? How does that change the OP "Universe"? If someone in China searched the World for strange happenings and found a group in Uzbekistan with all blue eyes, a Canadian would not care, or be surprised.

Certainly the OP would take more notice of a Canadian oddity.

Yes, and he has every right to.

Not being Canadian, I would assess it in a broader context…

I would not when discussing it with a Canadian.

English speaking world? Anywhere that has prime ministers? …

Practically nothing would be strange in a world of 8 billion people. That does not mean nothing is strange when limited to Canadian PMs.

 

[DaveC426913]

We need to know how the OP came across this factoid. Most likely (?) it was originally noticed by someone unknown to the OP and propagated through social media. This means we have to consider what oddities might be turned up by some population of Canadian amateur researchers.
Besides, I am not Canadian, so to me it falls in the same category as an equivalent factoid from anywhere in the world.

Yes, I encountered it on SocMed. Yes, I independently verified each PM myself.

As with all things nutritious and science-y - you don't have to take anyone's word for it. It takes about 90 seconds to Google 'What colour are [x]s eyes' ten times.

 

[Dale]

I think that your 1:10 number is far too low.

I described how I got there up above.

That is why I strongly suspect that Canadians have a bias for blue eyed PMs

I justified that up above too.

 

[FactChecker]

I described how I got there up above.


I justified that up above too.

1) the PM population has a significantly higher proportion of blue eyes

Yes. 100% in the last 50+ years is high. That is in the sample data. The question is what to conclude. I disagree with the contention that the result is due to a wide-spread fishing expedition for oddities.

 

[DaveC426913]

I start with the premise that physical appearance is important for political success.

That isn't sufficient - unless you pair it with the premise that blue-eyes positively influence appearance.

_{(I mean, the many girls in my life would attest that to be so, but that's just anecdotal.)}

 

[FactChecker]

That isn't sufficient - unless you pair it with the premise that blue-eyes positively influence appearance.

Your sample of data, together with the premise that an attractive appearance biases the results, can support the Hypothesis that blue eyes are attractive.

 

[Dale]

100% in the last 50+ years is high.

That is a deliberately biased sample, so I would avoid that whenever possible. But suppose that we did that anyway, what would we conclude?

With 10 of 10 blue-eyed PMs the posterior is $p \sim Beta(11,1)$ which has a 95 % credible interval from 0.715 to 0.998. Running that through the Monte Carlo simulation gives 559 out of 1000 runs with a maximum streak of at least 10 and obviously 0 runs with a maximum streak of at least 12.

I think that your 1:10 number is far too low.

It is not too far off, even using such a deliberately biased sample. 10/10 blue eyed PM's gives 0.559, while 22/24 gives 0.695, and 19/24 gives 0.227. The exact number depends strongly on the data, of course, but it is on the order of one in ten, not ten million.

 

[sbrothy]

Of course. No one doubts the correlation between gender and presidentness. Extremely gender-biased.

But eye-colour? What's weird is that there seems to be a strong correlation yet no readily available explanation as to why.

The most obvious (if not the most defensible) is the most direct: Canadians just simply prefer blue-eyed people, whether or not they know why.

I doubt this. I doubt Canadians are choosing their leader by eye-colour. But I don't have any theories about any indirect causes that might provide a correlation. It's not like Canadians have an affinity for Aryan politics or anything...


Best guess is that Canada's leadership has been largely drawn from well-educated and wealthy Northern European and British stock, where there is a higher proportion of blue eyes.




View attachment 375323

https://en.wikipedia.org/wiki/Eye_color




TIL:
Rayleigh Scattering might be at the heart of my sky blue eyes.

"One possible explanation for the difference in appearance between gray and blue eyes is that gray eyes have larger deposits of collagen in the stroma, so that the light that is reflected from the epithelium undergoes Mie scattering (which is not strongly frequency-dependent) rather than Rayleigh scattering (in which shorter wavelengths of light are scattered more). This would be analogous to the change in the color of the sky, from the blue given by the Rayleigh scattering of sunlight by small gas molecules when the sky is clear, to the gray caused by Mie scattering of large water droplets when the sky is cloudy."

“Presidentness”?

You people are all crazy!

 

[FactChecker]

But eye-colour? What's weird is that there seems to be a strong correlation yet no readily available explanation as to why.

Yes, eye-color. In some countries, if a politician wears a tan suit, large groups will make fun of it for years. It's sad. (sigh)

 

[haruspex]

Yes, eye-color. In some countries, if a politician wears a tan suit, large groups will make fun of it for years. It's sad. (sigh)

Maybe one could collect data on elected leaders' eye colours starting from before colour images (tv, newspapers) were widely available and see a trend.

 

[mfb]

Maybe, but ~1:10 to ~1:100 odd rather than ~1:1000000 to ~1:10000000 odd, even within that scope.

Only if you already accept the unusual observation of an eye color / PM correlation as a given.
If we start with the assumption of no correlation then the observation "the last 10 PMs had blue eyes" is extremely odd: This observation strongly suggests a correlation. A much higher chance of blue eyes among PMs is favored by a factor ~10⁶ by our evidence (growing to ~10⁹ by adding earlier PMs).

 

[Dale]

Only if you already accept the unusual observation of an eye color / PM correlation as a given.

I am not sure what random variables you are describing here that you think I am assuming are correlated.

My model had only two random variables: $x$ (the color of a given PM’s eyes with 1 being blue and 0 being not blue) and $p$ (the probability of blue eyes in the population of PMs). Since $E(x)=p$ they are indeed correlated. So the assumed correlation in my model is between the color of an individual PM’s eyes and the probability of blue eyes in the population of PMs. Do you object to that correlation? If so, why?

If we start with the assumption of no correlation

No correlation between what and what? Correlations are always between two random variables. I find it hard to believe that the correlation between $x$ and $p$ is objectionable.

Other than the model, which is very simple, the only other place that assumptions can reside is in the priors. Here, I used the standard uninformed prior. So I did not add any extra assumptions there.

A much higher chance of blue eyes among PMs is favored by a factor ~106 by our evidence (growing to ~109 by adding earlier PMs).

I would welcome a fully specified model and calculation that shows that. I think you will find that it will require some strong assumptions to get there.