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Using logistic regression that way isn't going to do much, since each city has a single nonzero independent variable.

I'd try something like this, stats wise. It is just 10 minutes of effort, but accounts for the different sample sizes. I added one success and failure to each city, i.e. Laplace smoothing. Then I computed a 95% percent confidence interval for each, using binom.test in R (i.e. binom.test(8,9)$conf.int). I sorted by the lower bound.

If the lower bound of one city is above the upper bound of another, then you can say it is a better place, using your metric.

                             x+1     n+2     lb      x1/n2   ub
     Mountain View, CA USA   144     209     0.621   0.689   0.751
     South San Francisco, CA 33      44      0.597   0.750   0.868
     Cambridge, MA USA       103     173     0.518   0.595   0.669
     Chapel Hill, NC USA     8       9       0.518   0.889   0.997
     Waltham, MA USA         61      101     0.502   0.604   0.700
     Cupertino, CA USA       38      60      0.499   0.633   0.754
     Foster City, CA USA     16      22      0.498   0.727   0.893
     San Mateo, CA USA       88      159     0.473   0.553   0.632
     San Jose, CA USA        112     208     0.468   0.538   0.608
     New York, NY USA        399     809     0.458   0.493   0.528
     San Bruno, CA USA       14      20      0.457   0.700   0.881
     Palo Alto, CA USA       128     246     0.456   0.520   0.584
     Itasca, IL USA          8       10      0.444   0.800   0.975
     Westford, MA USA        8       10      0.444   0.800   0.975
     Los Gatos, CA USA       14      21      0.430   0.667   0.854
     Arlington, VA USA       15      23      0.427   0.652   0.836
     Aliso Viejo, CA USA     16      25      0.425   0.640   0.820
     Branford, CT USA        6       7       0.421   0.857   0.996
     Milpitas, CA USA        22      37      0.421   0.595   0.752
     Alameda, CA USA         10      14      0.419   0.714   0.916
     Redwood City, CA USA    64      126     0.417   0.508   0.598
     Austin, TX USA          115     242     0.411   0.475   0.540
     Berlin, 16 DEU          16      27      0.388   0.593   0.776
     Chelmsford, MA USA      9       13      0.386   0.692   0.909
     Portland, OR USA        36      71      0.386   0.507   0.628
     Tel Aviv, 5 ISR         38      76      0.383   0.500   0.617
     Pasadena, CA USA        21      38      0.383   0.553   0.714
     Fremont, CA USA         40      81      0.381   0.494   0.607
     Boulder, CO USA         40      85      0.361   0.471   0.582
     Morrisville, NC USA     20      38      0.358   0.526   0.690
     Marlborough, MA USA     16      29      0.357   0.552   0.736
     El Segundo, CA USA      10      16      0.354   0.625   0.848
     Sterling, VA USA        9       14      0.351   0.643   0.872
     Richardson, TX USA      18      34      0.351   0.529   0.702
     Bethesda, MD USA        18      34      0.351   0.529   0.702
     Burlington, ON CAN      6       8       0.349   0.750   0.968
     Oak Brook, IL USA       6       8       0.349   0.750   0.968
     Solana Beach, CA USA    6       8       0.349   0.750   0.968
     Venice, CA USA          8       12      0.349   0.667   0.901
     Belmont, CA USA         8       12      0.349   0.667   0.901
     Vancouver, BC CAN       45      101     0.347   0.446   0.548
     Atlanta, GA USA         58      140     0.332   0.414   0.501
     Montreal, QC CAN        29      64      0.328   0.453   0.583
     London, H9 GBR          131     358     0.316   0.366   0.418
     Kfar Saba, 2 ISR        8       13      0.316   0.615   0.861
     Ottawa, ON CAN          24      53      0.316   0.453   0.596
     Irvine, CA USA          44      108     0.314   0.407   0.506
     Mclean, VA USA          15      30      0.313   0.500   0.687
     Minneapolis, MN USA     23      51      0.311   0.451   0.597
     Beverly Hills, CA USA   10      18      0.308   0.556   0.785
     Toronto, ON CAN         60      157     0.306   0.382   0.463
     Surry Hills, 2 AUS      6       9       0.299   0.667   0.925
     Kitchener, ON CAN       6       9       0.299   0.667   0.925
     Doylestown, PA USA      5       7       0.290   0.714   0.963
     Ames, IA USA            5       7       0.290   0.714   0.963
     Salt Lake City, UT USA  27      66      0.290   0.409   0.537
     Irving, TX USA          10      19      0.289   0.526   0.756
     Gaithersburg, MD USA    10      19      0.289   0.526   0.756
     Tokyo, 40 JPN           24      58      0.286   0.414   0.551
     Gent, 8 BEL             4       5       0.284   0.800   0.995
     Fuzhou Shi, 3 CHN       4       5       0.284   0.800   0.995
     Lake Forest, IL USA     4       5       0.284   0.800   0.995
     Sunrise, FL USA         4       5       0.284   0.800   0.995
     Fredericton, NS CAN     4       5       0.284   0.800   0.995
     Princeton, NJ USA       11      22      0.282   0.500   0.718
     Baltimore, MD USA       15      33      0.281   0.455   0.636
     Paris, A8 FRA           57      161     0.280   0.354   0.433
     Wilmington, DE USA      9       17      0.278   0.529   0.770
     San Antonio, TX USA     14      31      0.273   0.452   0.640
     Beijing, 22 CHN         46      130     0.272   0.354   0.442
     Oakland, CA USA         16      37      0.271   0.432   0.605
     Hamburg, 4 DEU          12      26      0.266   0.462   0.666
     Westminster, CO USA     8       15      0.266   0.533   0.787
     Philadelphia, PA USA    20      50      0.264   0.400   0.548
     Houston, TX USA         36      101     0.264   0.356   0.458
     Cambridge, C3 GBR       18      44      0.263   0.409   0.568
     Ann Arbor, MI USA       14      33      0.255   0.424   0.608

"Did you win the Putnam?"

Yes, I did.


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