L. A. Is the Best American City --Just Ask a Seattle Social Scientist : Migration: Californians flood the Pacific Northwest. A dumb move, according to the Weber-Fechner Law of psychological analysis.

SEATTLE —  The city of Seattle is undergoing a collective civic shudder these days as Californians, weary of their native land, relocate here by the thousands. This migration, along with the local anti-growth sentiment--and anti-California sentiment begot by it--has incited a flurry of national media interest in major magazines and newspapers.

Why Seattle? Why don’t disgruntled Angelenos resettle in warmer, drier, traditionally receptive Sun Belt Edens such as Orlando or Phoenix or Albuquerque rather than the drizzly backwaters of the Pacific Northwest?

I believe one answer to this moving mystery lies in the unending parade of “best places” lists that put Seattle at or near the top. If you believe the lists, you conclude that Seattle is America’s hot city.

The most recent ranking appears in the new edition of “The Places Rated Almanac,” where Seattle emerges as the No. 1 U.S. urban area in terms of overall livability. I read this and imagined new waves of immigrants, bringing yet more traffic congestion, yet higher housing costs to this beleaguered landfall.

Then I decided to scrutinize the basis of the almanac rankings, not as a proud Seattlite in panic but as a research scientist who investigates how people interpret information to arrive at opinions and attitudes. What I found was quite provocative, leading me to conclude that Californians would be much better off staying where they are. Let me explain.

To compile their standings, from 1 (best) to 333 (worst), almanac authors added up the figures for nine living conditions at each location. The lower that sum, the better the city. Seattle wound up with a 666 total and was accordingly proclaimed best of all.

This appears pretty straightforward, using simple addition to find the sum of “goodness.” Hidden within this apparently innocent and reasonable technique, however, is a major compilation problem that makes the result invalid.

Let me illustrate by example, comparing two cities: San Francisco and Galveston. For simplicity, just consider two categories: climate and crime, because the logic would be the same using all 333 cities and all nine categories.

First, climate. San Francisco is ranked No. 1, supposedly the best in the country. Muggy Galveston, by contrast, is ranked No. 20. Psychologically, there is a big difference between being No. 1 and being No. 20. If you put yourself in San Francisco, you would have every right to think San Francisco has a much better climate than Galveston, remembering how many other places are ahead of the Texas city.

Next, crime. San Francisco is ranked 290, while Galveston is ranked 268. In other words, both cities are pretty terrible in terms of crime. But psychologically, they’re quite similar. Psychologically, the difference between 268 and 290 isn’t all that big. If you put yourself in either place, you would have every right to worry.

Then where are we? With respect to climate, San Francisco is psychologically much better than Galveston. But with respect to crime, the two cities are psychologically similar. Overall, then, San Francisco would seem to be superior.

Yet that is not what you’d conclude by using “The Places Rated Almanac” technique of summing ranks. Galveston’s sum (20 + 268 = 288) is lower than San Francisco’s (1 + 290 = 291). So adding up rankings leads to the psychologically inappropriate conclusion that Galveston is better than San Francisco.

You can avoid this problem if you produce a city’s overall-goodness score by multiplying ranks--to get a product--rather than by adding them to get a sum. If we use products, San Francisco comes out 1 x 290 = 290, lower than Galveston’s 20 x 268 = 5360. So applying products rather than sums leads to the appropriate conclusion that San Francisco is a better place to live than Galveston.

Why are products better than sums in discovering goodness scores? The answer revolves around a venerable psychological principle, the Weber-Fechner Law, which says that with any physical scale, a particular numerical difference is psychologically more important at the low end than at the high end. For instance, the brightness difference between one and 20 light bulbs in an otherwise dark room is psychologically--and visibly--more important than the same 19-bulb difference between 271 and 290 light bulbs. The size difference between a four-pound infant and a nine-pound infant is demonstrably more apparent than the same weight difference between a 272-pound linebacker and a 277-pound linebacker.

Then what are the best cities under the Weber-Fechner Law? I have used the almanac’s raw data to calculate products of overall goodness for each of the 333 cities. Here are the top 10 cities, with almanac results in parentheses:

1. Los Angeles (15)

2. New York City (7)

3. San Francisco (2)

4. Chicago (18)

5. Washington (4)

6. Anaheim/Santa Ana (9)

7. Seattle (1)

8. San Diego (5)

9. Boston (6)

10. Oakland (10)

When you use the psychologically valid technique, Seattle drops to seventh place, outranked by three California cities, with Los Angeles as the new No 1.

I mentioned this scientific finding to a friend from Los Angeles. He was skeptical. “But you don’t want people moving to Seattle,” he said. “You have a vested interest in Seattle not being ranked first.”

I do have a vested interest. But numbers don’t lie. Anyone with a calculator will get the same result.

The message from this Seattlite to his California brethren is clear: Congratulations on having such wonderful cities in such a wonderful state. You’re better than Seattle. So stay where you are.