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Instead of you (or anyone) prioritising, could you calculate the median population  served per mile for each link, as a rough indication of which links are likely to be built first?

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Sun Mar 25th, 2007 at 06:23:05 AM EST
[ Parent ]
Is there a difference between median and mean population when looking at the two ends of the links?

Anyway, the answer is, yes, I can do both the arithmatic and the geometric mean per mile of each pair ... I'm getting on that right now.


I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Sun Mar 25th, 2007 at 07:33:43 AM EST
[ Parent ]
I meant geometric mean...

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Sun Mar 25th, 2007 at 05:00:06 PM EST
[ Parent ]
Oh ... hey, that's the one I posted!

I did the arithmatic mean first, but it is just the sum scaled by a factor of 0.5. But since the central place hierarchy tends to be a log-linear relationship, the geometric mean felt like it was probably better.

And who knows ... one day in the distant past I may have actually read some literature that suggested that the geometric mean is the preferable measure in general for this situation ... I definitely knew a lot more abstract regional economics stuff a decade ago, even if I knew a lot less about the real world problems of fighting for better public transport.

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Mon Mar 26th, 2007 at 10:02:48 AM EST
[ Parent ]
The geometric mean is better for quantities that are necessarily positive (like population), or that grow multiplicatively (like population).

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 10:04:55 AM EST
[ Parent ]
Maybe ... I'm more a picking the tool to fit the problem kind of economist, so I would say that in this case, that fact that the size of the other city in the pair is a main factor in determing the percentage market share leads one into the logarithmic family. Its a main reason why the ratio of populations between adjoining levels of the central place hierarchy tends to be close to constant (for most developed economies). And in the logarithmic family, the simplest mean is:

antilog( (log(x1)+log(x2))/2 )

which in direct arithmatic is:

(x1*x2)^.5

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Mon Mar 26th, 2007 at 11:03:05 AM EST
[ Parent ]
Exactly.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 05:34:49 PM EST
[ Parent ]
This is the trip geometric mean population per mile. Line of site miles are adjusted to assume an effective alignment that is 90% of the ideal alignment. All values are pairwise values, so obviously overlapping routes will pool infrastructure costs between these trips.

Lower cutoff at 100 miles, upper cutoff at 580 miles, all values to geo-mean 10,000/mile.

39,508 New York / Boston
37,435 Los Angeles / San Diego
33,476 New York / Philadelphia
31,627 New York / Baltimore
27,073 New York / Providence
21,625 Chicago / Detroit
20,978 New York / Washington
18,013 Chicago / Indianapolis
15,923 Dallas / Houston
14,717 Los Angeles / Phoenix
14,335 Orlando / Tampa
14,285 Los Angeles / Las Vegas
13,777 Washington / Virginia Beach
12,687 Seattle / Portland
12,625 New York / Cleveland
12,506 Washington / Pittsburgh
11,828 Indianapolis / Cincinatti
11,140 Houston / San Antonio
11,114 Chicago / Cleveland
10,901 Miami / Orlando
10,333 Chicago / Minneapolis

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Sun Mar 25th, 2007 at 11:44:49 AM EST
[ Parent ]

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