Comments on FiveThirtyEight: Politics Done Right: Homework Assignment

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2009-10-09T03:25:26.316-04:00

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2009-09-09T23:48:22.289-04:00

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2009-02-11T22:52:00.000-05:00

If we first add the states with the most EVs (from...

2008-06-22T19:21:00.000-04:00

If we first add the states with the most EVs (from the top down) we get 271 with the top 11 (so that's one). This means we need strictly more than 10 (this eliminates and partition of 10 or less states automatically).

Next we start at the bottom and reach 270+ with 41 so ANY partition of 41 or more will win. That's (51 choose 41 + 51 choose 42 + etc..) 16,593,192,942 different partitions according to the Google calculator.

I found some maple code (matlab would be better but this was lying around and I have free access to a cluster at work anyway) that will enumerate subsets. If it runs as fast as the author claims I should be able to simply make the computer(s) enumerate subsets (in the 12-40 range), add up each and print only those that add to 270+. This is really dirty but noone said anything about efficiently finding a solution :)

One time I drank so much plonk that I saw God. Or ...

2008-06-13T14:49:00.000-04:00

One time I drank so much plonk that I saw God. Or was it absinthe that I drank? Hmm. I don't really remember. And was it God or a monkey? And ...

Just for the record, I saw a barrel of monkeys onc...

2008-06-13T02:22:00.000-04:00

Just for the record, I saw a barrel of monkeys once.

jqb, it's okay if you like plonk -- after all, we ...

2008-06-12T22:33:00.000-04:00

jqb, it's okay if you like plonk -- after all, we ARE Democrats -- but I prefer the good stuff. Salut!

For those interested, here is an implementation in...

2008-06-12T21:18:00.000-04:00

For those interested, here is an implementation in LISP.
Takes 80 ms to find the correct number (51199463116367)

(defvar *ev-count* (make-array '(60 300)))

(defvar *evs* (list 9 3 10 6 55 9 7 3 3 27 15 4 4
21 11 7 6 8 9 4 10 12 17 10 6 11 3
5 5 4 15 5 31 15 3 20 7 7 21 4 8 3
11 34 5 3 13 11 5 10 3
))

(defun init-ev-count ()
(setq *ev-count* (make-array '(60 300))))

(defun ev-count (ev-list total)
(cond ((> total (apply #'+ ev-list))
0)
((< total 0)
0)
((= total 0)
1)
((aref *ev-count* (length ev-list) total))
(t (setf (aref *ev-count* (length ev-list) total)
(+ (ev-count (cdr ev-list) total)
(ev-count (cdr ev-list) (- total (car ev-list))))))))

(defun ev-count-unique (ev-list total min-ev)
(init-ev-count)
(let ((sufficient-evs (remove-if #'(lambda (ev) (< ev min-ev))
ev-list)))
(ev-count sufficient-evs total)))

(defun ev-count-total (ev-list total)
(loop for ev-min from 1 to 55
sum (ev-count-unique ev-list (+ (1- total) ev-min) ev-min)))

Charles Pluckhahn said...* PLONK *

2008-06-12T20:16:00.000-04:00

Charles Pluckhahn said...

* PLONK *

jqb, you're more fun than a barrel of monkeys. Of ...

2008-06-12T20:03:00.000-04:00

jqb, you're more fun than a barrel of monkeys. Of course, there is no such thing as a barrel of monkeys, so I'd better stop lying about that, too.

together with the other co-inventor, co-inventor, ...

2008-06-12T19:53:00.000-04:00

together with the other co-inventor, co-inventor, Bob Kahn, that Al Gore's statements

Make that "together with the other co-inventor, Bob Kahn, wrote that ..."

Specifically:
http://www.theregister.co.uk/2000/10/02/net_builders_kahn_cerf_recognise/

"""
Al Gore and the Internet

By Robert Kahn and Vinton Cerf

Al Gore was the first political leader to recognize the importance of the Internet and to promote and support its development.

No one person or even small group of persons exclusively "invented" the Internet. It is the result of many years of ongoing collaboration among people in government and the university community. But as the two people who designed the basic architecture and the core protocols that make the Internet work, we would like to acknowledge VP Gore's contributions as a Congressman, Senator and as Vice President. No other elected official, to our knowledge, has made a greater contribution over a longer period of time.

Last year the Vice President made a straightforward statement on his role. He said: "During my service in the United States Congress I took the initiative in creating the Internet." We don't think, as some people have argued, that Gore intended to claim he "invented" the Internet. Moreover, there is no question in our minds that while serving as Senator, Gore's initiatives had a significant and beneficial effect on the still-evolving Internet. The fact of the matter is that Gore was talking about and promoting the Internet long before most people were listening. We feel it is timely to offer our perspective.

As far back as the 1970s Congressman Gore promoted the idea of high speed telecommunications as an engine for both economic growth and the improvement of our educational system. He was the first elected official to grasp the potential of computer communications to have a broader impact than just improving the conduct of science and scholarship. Though easily forgotten now, at the time this was an unproven and controversial concept. Our work on the Internet started in 1973 and was based on even earlier work that took place in the mid-late 1960s. But the Internet, as we know it today, was not deployed until 1983. When the Internet was still in the early stages of its deployment, Congressman Gore provided intellectual leadership by helping create the vision of the potential benefits of high speed computing and communication. As an example, he sponsored hearings on how advanced technologies might be put to use in areas like coordinating the response of government agencies to natural disasters and other crises.

As a Senator in the 1980s Gore urged government agencies to consolidate what at the time were several dozen different and unconnected networks into an "Interagency Network." Working in a bi-partisan manner with officials in Ronald Reagan and George Bush's administrations, Gore secured the passage of the High Performance Computing and Communications Act in 1991. This "Gore Act" supported the National Research and Education Network (NREN) initiative that became one of the major vehicles for the spread of the Internet beyond the field of computer science.
...
"""

jqb, if you've been on the Internet since Al Gore ...

2008-06-12T19:47:00.000-04:00

jqb, if you've been on the Internet since Al Gore invented it

I worked with Vint Cerf at UCLA -- you know, the co-inventor of TCP/IP -- who, together with the other co-inventor, co-inventor, Bob Kahn, that Al Gore's statements about his role in the creation of the internet were accurate, and that the the commercial internet would have been much longer in coming if not for Gore's efforts. So don't go propagating that lie, even in jest.

then you ought to know by now that a sense of humor helps.

Tell it to Mike He.

Hey, it's only a movie. Now put down the beaker, and step back from the ledge ...

Fuck off, you pompous ass. :-)

jqb, if you've been on the Internet since Al Gore ...

2008-06-12T19:15:00.000-04:00

jqb, if you've been on the Internet since Al Gore invented it, then you ought to know by now that a sense of humor helps. Hey, it's only a movie. Now put down the beaker, and step back from the ledge ...

In case anyone might have a use for it, here's my ...

2008-06-12T18:08:00.000-04:00

In case anyone might have a use for it, here's my latest version of my program, cleaned up, commented, and sped up with the great pruning condition that Mike He mentioned:

#include <stdio.h>
#include <stdlib.h>

typedef unsigned long long Big;
typedef unsigned int Idx;
typedef unsigned int Votes;
typedef enum {
    US,         // states we will win
    THEM,       // states they will win
    PLAY        // states either might win
} Type;

typedef struct {
    char const* name;
    Votes       v;
    Type        type;
} State;

static Idx   n_of[3]; // number of states of type t
static Votes v_of[3]; // number of votes for states of type t

static State states[] = {
    {"AL",  9, THEM}, {"AK",  3, THEM}, {"AR", 10, THEM}, {"AZ",  6, THEM},
    {"CA", 55, US},   {"CO",  9, PLAY}, {"CT",  7, US},   {"DE",  3, US},
    {"DC",  3, US},   {"FL", 27, THEM}, {"GA", 15, THEM}, {"HI",  4, US},
    {"ID",  4, THEM}, {"IL", 21, US},   {"IN", 11, THEM}, {"IA",  7, PLAY},
    {"KS",  6, THEM}, {"KY",  8, THEM}, {"LA",  9, THEM}, {"ME",  4, US},
    {"MD", 10, US},   {"MA", 12, US},   {"MI", 17, PLAY}, {"MN", 10, US},
    {"MS",  6, THEM}, {"MO", 11, PLAY}, {"MT",  3, THEM}, {"NE",  5, THEM},
    {"NV",  5, PLAY}, {"NH",  4, PLAY}, {"NJ", 15, US},   {"NM",  5, PLAY},
    {"NY", 31, US},   {"NC", 15, THEM}, {"ND",  3, THEM}, {"OH", 20, PLAY},
    {"OK",  7, THEM}, {"OR",  7, US},   {"PA", 21, US},   {"RI",  4, US},
    {"SC",  8, THEM}, {"SD",  3, THEM}, {"TN", 11, THEM}, {"TX", 34, THEM},
    {"UT",  5, THEM}, {"VT",  3, US},   {"VA", 13, PLAY}, {"WA", 11, US},
    {"WV",  5, THEM}, {"WI", 10, PLAY}, {"WY",  3, THEM}
};

#define NSTATES (sizeof(states)/sizeof(*states))

static Votes    needed = 0;     // # of votes needed to win
static Votes    vsol = 0;       // # of votes in sol
static Big      nsol = 0;       // # of solutions
static Idx      sol[NSTATES];   // solution: indices into states

// find all of the solutions that consist of the states in sol[0..n-1]
// plus states from states[p..n_of[PLAY]-1];
// margin is # of votes available - needed
static void solve(Idx n, Idx p, int margin)
{
    if( vsol >= needed ){
        for( Idx i = 0; i < n; i++ )
            printf("%s ", states[sol[i]].name);
        printf("= %u (%u)\n", vsol, v_of[US] + vsol);
        nsol++;
        return;
    }

    // add each of p..n_of[PLAY]-1 in turn to sol
    while( p < n_of[PLAY] && margin >= 0 ){
        Votes v = states[sol[n] = p++].v;
        vsol += v;
        solve(n+1, p, margin);
        vsol -= v;
        margin -= v; // votes of sol[n] are no longer available
    }
}

// print states of type t
static void prstates(char const* s, Type t)
{
    printf("%d %s:", n_of[t], s);

    for( Idx i = 0; i < NSTATES; i++ )
        if( states[i].type == t )
            printf(" %s", states[i].name);

    printf(" = %u", v_of[t]);
    if( t == US ) printf(", %u more needed", needed);
    printf("\n");
}

// put PLAY states before non-PLAY states;
// order PLAY states by descending vote count
static int cmp(void const* a, void const* b)
{
    State* x = (State*)a;
    State* y = (State*)b;

    return(x->type == PLAY
           ? (y->type == PLAY
              ? (int)(y->v - x->v)
              : -1)
           : (y->type == PLAY
              ? 1
              : 0));
}

int main(void)
{
    for( Idx i = 0; i < NSTATES; i++ ){
        Type t = states[i].type;
        n_of[t]++;
        v_of[t] += states[i].v;
        needed += states[i].v;
    }

    needed = needed/2 + 1 - v_of[US];

    prstates("safe", US);
    prstates("out of reach", THEM);
    prstates("in play", PLAY);

    qsort(states, NSTATES, sizeof *states, cmp);
    solve(0, 0, v_of[PLAY] - needed);

    printf("%llu solutions\n", nsol);
    return 0;
}

P.S. I've been on the 'net for nearly 40 years (I ...

2008-06-12T18:02:00.000-04:00

P.S. I've been on the 'net for nearly 40 years (I was at UCLA when they installed the IMP) and have seen plenty of these emotionally immature people go all ad hominem, getting into whines about people's "tone" and and complaining about being condescended to (fragile ego much?), but I think this is the thinnest and least justified case I've ever seen. Perhaps Mike is just upset that his program is still running, and will be, for days -- it's an empirical fact, and kicking and screaming at the messenger won't change it.

Wow, I must say that I am completely turned off by...

2008-06-12T17:51:00.000-04:00

Wow, I must say that I am completely turned off by jqb's condescending, smug attitude. What originally was a fun thought problem for a group to tackle has turned into a snarky comment laden page of trying to prove one's own intelligence and insult that of others. jqb, you may think that you're pretty smart, but that sort of attitude simply isn't respectful, and it certainly won't earn you respect. No need to comment back or argue with me, jqb, as I'm just going to just leave it at that and have lost interest in this thread.

What a pathetic little crybaby. You're as bad as all those women who are going to vote for McCain because their feelings are hurt. The fact is that you're totally off base and are projecting, because comments of mine, like "Sorry to have been so dense, and so sloppy that I didn't even notice how absurd the results were" is not condescending or smug in any honest person's book.

Wow, I must say that I am completely turned off by...

2008-06-12T15:32:00.000-04:00

Wow, I must say that I am completely turned off by...

2008-06-12T14:28:00.000-04:00

dont know if this has been covered before, but is ...

2008-06-12T11:42:00.000-04:00

dont know if this has been covered before, but is more likely than others. obama holds all kerry states accept hew hampshire, but wins iowa, colorado, and new mexico (currently leads in all 3) this would be 269, but if he picks up one electoral vote from splitting nebraska (winning the omaha district) that would be exactly 270.

P.S. those 3 281's come from55 34 31 27 21 21 20 1...

2008-06-12T10:13:00.000-04:00

P.S. those 3 281's come from

55 34 31 27 21 21 20 17 15 15 13 12

There are three such combinations, for the three different pairs taken from GA, NC, and NJ, each with 15 EVs. Why someone would think that the totals can only be 270, 271, or 272 is beyond me.

Answer: 115 unique waysSigh. You might try reading...

2008-06-12T09:48:00.000-04:00

Answer: 115 unique ways

Sigh. You might try reading some of the other comments before posting.

unique solutions to
270: 38
271: 39
272: 38

Uh, no. In fact,

270: 17054665123395
271: 17046339123934
272: 17032469851307
273: 64077397366
274: 1856215791
275: 49806934
276: 5308169
277: 239471
278: 46351
279: 3568
280: 78
281: 3

Answer: 115 unique waysunique solutions to270: 382...

2008-06-12T09:42:00.000-04:00

Answer: 115 unique ways

unique solutions to
270: 38
271: 39
272: 38

ruby script to solve problem:
#! /usr/bin/env ruby

@votes = [55,34,31,27,21,21,20,17,15,15,15,13,12,11,11,11,11,10,10,10,10,9,9,9,8,8,7,7,7,7,6,6,6,5,5,5,5,5,4,4,4,4,4,3,3,3,3,3,3,3,3]
@results = Array.new(273, 0)
@results[0] = 1

@votes.each_index { |i|
272.downto(0) do |j|
if (@results[j] > 0)
newTotal = @votes[i] +j
if (newTotal <= 272)
@results[newTotal]+=1
end
end
end
}

puts @results[270]
puts @results[271]
puts @results[272]

P.S.OH MI VA MO WI CO IA NV NM NH = 101 (322)Would...

2008-06-12T08:24:00.000-04:00

P.S.

OH MI VA MO WI CO IA NV NM NH = 101 (322)

Wouldn't it be sweet.

To make the point, I ran it with the constraint r...

2008-06-12T08:18:00.000-04:00

To make the point, I ran it with the constraint removed, and now the frequency of the occurrence of a state is, as one should expect, in accord with its number of EVs: OH MI VA MO WI ...

17 safe: CA CT DE DC HI IL ME MD MA MN NJ NY OR PA RI VT WA = 221, 49 more needed
24 out of reach: AL AK AR AZ FL GA ID IN KS KY LA MS MT NE NC ND OK SC SD TN TX UT WV WY = 216
10 in play: CO IA MI MO NV NH NM OH VA WI = 101
OH MI VA = 50 (271)
OH MI VA MO = 61 (282)
OH MI VA MO WI = 71 (292)
OH MI VA MO WI CO = 80 (301)
OH MI VA MO WI CO IA = 87 (308)
OH MI VA MO WI CO IA NV = 92 (313)
OH MI VA MO WI CO IA NV NM = 97 (318)
OH MI VA MO WI CO IA NV NM NH = 101 (322)
OH MI VA MO WI CO IA NV NH = 96 (317)
OH MI VA MO WI CO IA NM = 92 (313)
OH MI VA MO WI CO IA NM NH = 96 (317)
OH MI VA MO WI CO IA NH = 91 (312)
OH MI VA MO WI CO NV = 85 (306)
OH MI VA MO WI CO NV NM = 90 (311)
OH MI VA MO WI CO NV NM NH = 94 (315)
OH MI VA MO WI CO NV NH = 89 (310)
OH MI VA MO WI CO NM = 85 (306)
OH MI VA MO WI CO NM NH = 89 (310)
OH MI VA MO WI CO NH = 84 (305)
OH MI VA MO WI IA = 78 (299)
OH MI VA MO WI IA NV = 83 (304)
OH MI VA MO WI IA NV NM = 88 (309)
OH MI VA MO WI IA NV NM NH = 92 (313)
OH MI VA MO WI IA NV NH = 87 (308)
OH MI VA MO WI IA NM = 83 (304)
OH MI VA MO WI IA NM NH = 87 (308)
OH MI VA MO WI IA NH = 82 (303)
OH MI VA MO WI NV = 76 (297)
OH MI VA MO WI NV NM = 81 (302)
OH MI VA MO WI NV NM NH = 85 (306)
OH MI VA MO WI NV NH = 80 (301)
OH MI VA MO WI NM = 76 (297)
OH MI VA MO WI NM NH = 80 (301)
OH MI VA MO WI NH = 75 (296)
OH MI VA MO CO = 70 (291)
OH MI VA MO CO IA = 77 (298)
OH MI VA MO CO IA NV = 82 (303)
OH MI VA MO CO IA NV NM = 87 (308)
OH MI VA MO CO IA NV NM NH = 91 (312)
OH MI VA MO CO IA NV NH = 86 (307)
OH MI VA MO CO IA NM = 82 (303)
OH MI VA MO CO IA NM NH = 86 (307)
OH MI VA MO CO IA NH = 81 (302)
OH MI VA MO CO NV = 75 (296)
OH MI VA MO CO NV NM = 80 (301)
OH MI VA MO CO NV NM NH = 84 (305)
OH MI VA MO CO NV NH = 79 (300)
OH MI VA MO CO NM = 75 (296)
OH MI VA MO CO NM NH = 79 (300)
OH MI VA MO CO NH = 74 (295)
OH MI VA MO IA = 68 (289)
OH MI VA MO IA NV = 73 (294)
OH MI VA MO IA NV NM = 78 (299)
OH MI VA MO IA NV NM NH = 82 (303)
OH MI VA MO IA NV NH = 77 (298)
OH MI VA MO IA NM = 73 (294)
OH MI VA MO IA NM NH = 77 (298)
OH MI VA MO IA NH = 72 (293)
OH MI VA MO NV = 66 (287)
OH MI VA MO NV NM = 71 (292)
OH MI VA MO NV NM NH = 75 (296)
OH MI VA MO NV NH = 70 (291)
OH MI VA MO NM = 66 (287)
OH MI VA MO NM NH = 70 (291)
OH MI VA MO NH = 65 (286)
OH MI VA WI = 60 (281)
OH MI VA WI CO = 69 (290)
OH MI VA WI CO IA = 76 (297)
OH MI VA WI CO IA NV = 81 (302)
OH MI VA WI CO IA NV NM = 86 (307)
OH MI VA WI CO IA NV NM NH = 90 (311)
OH MI VA WI CO IA NV NH = 85 (306)
OH MI VA WI CO IA NM = 81 (302)
OH MI VA WI CO IA NM NH = 85 (306)
OH MI VA WI CO IA NH = 80 (301)
OH MI VA WI CO NV = 74 (295)
OH MI VA WI CO NV NM = 79 (300)
OH MI VA WI CO NV NM NH = 83 (304)
OH MI VA WI CO NV NH = 78 (299)
OH MI VA WI CO NM = 74 (295)
OH MI VA WI CO NM NH = 78 (299)
OH MI VA WI CO NH = 73 (294)
OH MI VA WI IA = 67 (288)
OH MI VA WI IA NV = 72 (293)
OH MI VA WI IA NV NM = 77 (298)
OH MI VA WI IA NV NM NH = 81 (302)
OH MI VA WI IA NV NH = 76 (297)
OH MI VA WI IA NM = 72 (293)
OH MI VA WI IA NM NH = 76 (297)
OH MI VA WI IA NH = 71 (292)
OH MI VA WI NV = 65 (286)
OH MI VA WI NV NM = 70 (291)
OH MI VA WI NV NM NH = 74 (295)
OH MI VA WI NV NH = 69 (290)
OH MI VA WI NM = 65 (286)
OH MI VA WI NM NH = 69 (290)
OH MI VA WI NH = 64 (285)
OH MI VA CO = 59 (280)
OH MI VA CO IA = 66 (287)
OH MI VA CO IA NV = 71 (292)
OH MI VA CO IA NV NM = 76 (297)
OH MI VA CO IA NV NM NH = 80 (301)
OH MI VA CO IA NV NH = 75 (296)
OH MI VA CO IA NM = 71 (292)
OH MI VA CO IA NM NH = 75 (296)
OH MI VA CO IA NH = 70 (291)
OH MI VA CO NV = 64 (285)
OH MI VA CO NV NM = 69 (290)
OH MI VA CO NV NM NH = 73 (294)
OH MI VA CO NV NH = 68 (289)
OH MI VA CO NM = 64 (285)
OH MI VA CO NM NH = 68 (289)
OH MI VA CO NH = 63 (284)
OH MI VA IA = 57 (278)
OH MI VA IA NV = 62 (283)
OH MI VA IA NV NM = 67 (288)
OH MI VA IA NV NM NH = 71 (292)
OH MI VA IA NV NH = 66 (287)
OH MI VA IA NM = 62 (283)
OH MI VA IA NM NH = 66 (287)
OH MI VA IA NH = 61 (282)
OH MI VA NV = 55 (276)
OH MI VA NV NM = 60 (281)
OH MI VA NV NM NH = 64 (285)
OH MI VA NV NH = 59 (280)
OH MI VA NM = 55 (276)
OH MI VA NM NH = 59 (280)
OH MI VA NH = 54 (275)
OH MI MO WI = 58 (279)
OH MI MO WI CO = 67 (288)
OH MI MO WI CO IA = 74 (295)
OH MI MO WI CO IA NV = 79 (300)
OH MI MO WI CO IA NV NM = 84 (305)
OH MI MO WI CO IA NV NM NH = 88 (309)
OH MI MO WI CO IA NV NH = 83 (304)
OH MI MO WI CO IA NM = 79 (300)
OH MI MO WI CO IA NM NH = 83 (304)
OH MI MO WI CO IA NH = 78 (299)
OH MI MO WI CO NV = 72 (293)
OH MI MO WI CO NV NM = 77 (298)
OH MI MO WI CO NV NM NH = 81 (302)
OH MI MO WI CO NV NH = 76 (297)
OH MI MO WI CO NM = 72 (293)
OH MI MO WI CO NM NH = 76 (297)
OH MI MO WI CO NH = 71 (292)
OH MI MO WI IA = 65 (286)
OH MI MO WI IA NV = 70 (291)
OH MI MO WI IA NV NM = 75 (296)
OH MI MO WI IA NV NM NH = 79 (300)
OH MI MO WI IA NV NH = 74 (295)
OH MI MO WI IA NM = 70 (291)
OH MI MO WI IA NM NH = 74 (295)
OH MI MO WI IA NH = 69 (290)
OH MI MO WI NV = 63 (284)
OH MI MO WI NV NM = 68 (289)
OH MI MO WI NV NM NH = 72 (293)
OH MI MO WI NV NH = 67 (288)
OH MI MO WI NM = 63 (284)
OH MI MO WI NM NH = 67 (288)
OH MI MO WI NH = 62 (283)
OH MI MO CO = 57 (278)
OH MI MO CO IA = 64 (285)
OH MI MO CO IA NV = 69 (290)
OH MI MO CO IA NV NM = 74 (295)
OH MI MO CO IA NV NM NH = 78 (299)
OH MI MO CO IA NV NH = 73 (294)
OH MI MO CO IA NM = 69 (290)
OH MI MO CO IA NM NH = 73 (294)
OH MI MO CO IA NH = 68 (289)
OH MI MO CO NV = 62 (283)
OH MI MO CO NV NM = 67 (288)
OH MI MO CO NV NM NH = 71 (292)
OH MI MO CO NV NH = 66 (287)
OH MI MO CO NM = 62 (283)
OH MI MO CO NM NH = 66 (287)
OH MI MO CO NH = 61 (282)
OH MI MO IA = 55 (276)
OH MI MO IA NV = 60 (281)
OH MI MO IA NV NM = 65 (286)
OH MI MO IA NV NM NH = 69 (290)
OH MI MO IA NV NH = 64 (285)
OH MI MO IA NM = 60 (281)
OH MI MO IA NM NH = 64 (285)
OH MI MO IA NH = 59 (280)
OH MI MO NV = 53 (274)
OH MI MO NV NM = 58 (279)
OH MI MO NV NM NH = 62 (283)
OH MI MO NV NH = 57 (278)
OH MI MO NM = 53 (274)
OH MI MO NM NH = 57 (278)
OH MI MO NH = 52 (273)
OH MI WI CO = 56 (277)
OH MI WI CO IA = 63 (284)
OH MI WI CO IA NV = 68 (289)
OH MI WI CO IA NV NM = 73 (294)
OH MI WI CO IA NV NM NH = 77 (298)
OH MI WI CO IA NV NH = 72 (293)
OH MI WI CO IA NM = 68 (289)
OH MI WI CO IA NM NH = 72 (293)
OH MI WI CO IA NH = 67 (288)
OH MI WI CO NV = 61 (282)
OH MI WI CO NV NM = 66 (287)
OH MI WI CO NV NM NH = 70 (291)
OH MI WI CO NV NH = 65 (286)
OH MI WI CO NM = 61 (282)
OH MI WI CO NM NH = 65 (286)
OH MI WI CO NH = 60 (281)
OH MI WI IA = 54 (275)
OH MI WI IA NV = 59 (280)
OH MI WI IA NV NM = 64 (285)
OH MI WI IA NV NM NH = 68 (289)
OH MI WI IA NV NH = 63 (284)
OH MI WI IA NM = 59 (280)
OH MI WI IA NM NH = 63 (284)
OH MI WI IA NH = 58 (279)
OH MI WI NV = 52 (273)
OH MI WI NV NM = 57 (278)
OH MI WI NV NM NH = 61 (282)
OH MI WI NV NH = 56 (277)
OH MI WI NM = 52 (273)
OH MI WI NM NH = 56 (277)
OH MI WI NH = 51 (272)
OH MI CO IA = 53 (274)
OH MI CO IA NV = 58 (279)
OH MI CO IA NV NM = 63 (284)
OH MI CO IA NV NM NH = 67 (288)
OH MI CO IA NV NH = 62 (283)
OH MI CO IA NM = 58 (279)
OH MI CO IA NM NH = 62 (283)
OH MI CO IA NH = 57 (278)
OH MI CO NV = 51 (272)
OH MI CO NV NM = 56 (277)
OH MI CO NV NM NH = 60 (281)
OH MI CO NV NH = 55 (276)
OH MI CO NM = 51 (272)
OH MI CO NM NH = 55 (276)
OH MI CO NH = 50 (271)
OH MI IA NV = 49 (270)
OH MI IA NV NM = 54 (275)
OH MI IA NV NM NH = 58 (279)
OH MI IA NV NH = 53 (274)
OH MI IA NM = 49 (270)
OH MI IA NM NH = 53 (274)
OH MI NV NM NH = 51 (272)
OH VA MO WI = 54 (275)
OH VA MO WI CO = 63 (284)
OH VA MO WI CO IA = 70 (291)
OH VA MO WI CO IA NV = 75 (296)
OH VA MO WI CO IA NV NM = 80 (301)
OH VA MO WI CO IA NV NM NH = 84 (305)
OH VA MO WI CO IA NV NH = 79 (300)
OH VA MO WI CO IA NM = 75 (296)
OH VA MO WI CO IA NM NH = 79 (300)
OH VA MO WI CO IA NH = 74 (295)
OH VA MO WI CO NV = 68 (289)
OH VA MO WI CO NV NM = 73 (294)
OH VA MO WI CO NV NM NH = 77 (298)
OH VA MO WI CO NV NH = 72 (293)
OH VA MO WI CO NM = 68 (289)
OH VA MO WI CO NM NH = 72 (293)
OH VA MO WI CO NH = 67 (288)
OH VA MO WI IA = 61 (282)
OH VA MO WI IA NV = 66 (287)
OH VA MO WI IA NV NM = 71 (292)
OH VA MO WI IA NV NM NH = 75 (296)
OH VA MO WI IA NV NH = 70 (291)
OH VA MO WI IA NM = 66 (287)
OH VA MO WI IA NM NH = 70 (291)
OH VA MO WI IA NH = 65 (286)
OH VA MO WI NV = 59 (280)
OH VA MO WI NV NM = 64 (285)
OH VA MO WI NV NM NH = 68 (289)
OH VA MO WI NV NH = 63 (284)
OH VA MO WI NM = 59 (280)
OH VA MO WI NM NH = 63 (284)
OH VA MO WI NH = 58 (279)
OH VA MO CO = 53 (274)
OH VA MO CO IA = 60 (281)
OH VA MO CO IA NV = 65 (286)
OH VA MO CO IA NV NM = 70 (291)
OH VA MO CO IA NV NM NH = 74 (295)
OH VA MO CO IA NV NH = 69 (290)
OH VA MO CO IA NM = 65 (286)
OH VA MO CO IA NM NH = 69 (290)
OH VA MO CO IA NH = 64 (285)
OH VA MO CO NV = 58 (279)
OH VA MO CO NV NM = 63 (284)
OH VA MO CO NV NM NH = 67 (288)
OH VA MO CO NV NH = 62 (283)
OH VA MO CO NM = 58 (279)
OH VA MO CO NM NH = 62 (283)
OH VA MO CO NH = 57 (278)
OH VA MO IA = 51 (272)
OH VA MO IA NV = 56 (277)
OH VA MO IA NV NM = 61 (282)
OH VA MO IA NV NM NH = 65 (286)
OH VA MO IA NV NH = 60 (281)
OH VA MO IA NM = 56 (277)
OH VA MO IA NM NH = 60 (281)
OH VA MO IA NH = 55 (276)
OH VA MO NV = 49 (270)
OH VA MO NV NM = 54 (275)
OH VA MO NV NM NH = 58 (279)
OH VA MO NV NH = 53 (274)
OH VA MO NM = 49 (270)
OH VA MO NM NH = 53 (274)
OH VA WI CO = 52 (273)
OH VA WI CO IA = 59 (280)
OH VA WI CO IA NV = 64 (285)
OH VA WI CO IA NV NM = 69 (290)
OH VA WI CO IA NV NM NH = 73 (294)
OH VA WI CO IA NV NH = 68 (289)
OH VA WI CO IA NM = 64 (285)
OH VA WI CO IA NM NH = 68 (289)
OH VA WI CO IA NH = 63 (284)
OH VA WI CO NV = 57 (278)
OH VA WI CO NV NM = 62 (283)
OH VA WI CO NV NM NH = 66 (287)
OH VA WI CO NV NH = 61 (282)
OH VA WI CO NM = 57 (278)
OH VA WI CO NM NH = 61 (282)
OH VA WI CO NH = 56 (277)
OH VA WI IA = 50 (271)
OH VA WI IA NV = 55 (276)
OH VA WI IA NV NM = 60 (281)
OH VA WI IA NV NM NH = 64 (285)
OH VA WI IA NV NH = 59 (280)
OH VA WI IA NM = 55 (276)
OH VA WI IA NM NH = 59 (280)
OH VA WI IA NH = 54 (275)
OH VA WI NV NM = 53 (274)
OH VA WI NV NM NH = 57 (278)
OH VA WI NV NH = 52 (273)
OH VA WI NM NH = 52 (273)
OH VA CO IA = 49 (270)
OH VA CO IA NV = 54 (275)
OH VA CO IA NV NM = 59 (280)
OH VA CO IA NV NM NH = 63 (284)
OH VA CO IA NV NH = 58 (279)
OH VA CO IA NM = 54 (275)
OH VA CO IA NM NH = 58 (279)
OH VA CO IA NH = 53 (274)
OH VA CO NV NM = 52 (273)
OH VA CO NV NM NH = 56 (277)
OH VA CO NV NH = 51 (272)
OH VA CO NM NH = 51 (272)
OH VA IA NV NM = 50 (271)
OH VA IA NV NM NH = 54 (275)
OH VA IA NV NH = 49 (270)
OH VA IA NM NH = 49 (270)
OH MO WI CO = 50 (271)
OH MO WI CO IA = 57 (278)
OH MO WI CO IA NV = 62 (283)
OH MO WI CO IA NV NM = 67 (288)
OH MO WI CO IA NV NM NH = 71 (292)
OH MO WI CO IA NV NH = 66 (287)
OH MO WI CO IA NM = 62 (283)
OH MO WI CO IA NM NH = 66 (287)
OH MO WI CO IA NH = 61 (282)
OH MO WI CO NV = 55 (276)
OH MO WI CO NV NM = 60 (281)
OH MO WI CO NV NM NH = 64 (285)
OH MO WI CO NV NH = 59 (280)
OH MO WI CO NM = 55 (276)
OH MO WI CO NM NH = 59 (280)
OH MO WI CO NH = 54 (275)
OH MO WI IA NV = 53 (274)
OH MO WI IA NV NM = 58 (279)
OH MO WI IA NV NM NH = 62 (283)
OH MO WI IA NV NH = 57 (278)
OH MO WI IA NM = 53 (274)
OH MO WI IA NM NH = 57 (278)
OH MO WI IA NH = 52 (273)
OH MO WI NV NM = 51 (272)
OH MO WI NV NM NH = 55 (276)
OH MO WI NV NH = 50 (271)
OH MO WI NM NH = 50 (271)
OH MO CO IA NV = 52 (273)
OH MO CO IA NV NM = 57 (278)
OH MO CO IA NV NM NH = 61 (282)
OH MO CO IA NV NH = 56 (277)
OH MO CO IA NM = 52 (273)
OH MO CO IA NM NH = 56 (277)
OH MO CO IA NH = 51 (272)
OH MO CO NV NM = 50 (271)
OH MO CO NV NM NH = 54 (275)
OH MO CO NV NH = 49 (270)
OH MO CO NM NH = 49 (270)
OH MO IA NV NM NH = 52 (273)
OH WI CO IA NV = 51 (272)
OH WI CO IA NV NM = 56 (277)
OH WI CO IA NV NM NH = 60 (281)
OH WI CO IA NV NH = 55 (276)
OH WI CO IA NM = 51 (272)
OH WI CO IA NM NH = 55 (276)
OH WI CO IA NH = 50 (271)
OH WI CO NV NM = 49 (270)
OH WI CO NV NM NH = 53 (274)
OH WI IA NV NM NH = 51 (272)
OH CO IA NV NM NH = 50 (271)
MI VA MO WI = 51 (272)
MI VA MO WI CO = 60 (281)
MI VA MO WI CO IA = 67 (288)
MI VA MO WI CO IA NV = 72 (293)
MI VA MO WI CO IA NV NM = 77 (298)
MI VA MO WI CO IA NV NM NH = 81 (302)
MI VA MO WI CO IA NV NH = 76 (297)
MI VA MO WI CO IA NM = 72 (293)
MI VA MO WI CO IA NM NH = 76 (297)
MI VA MO WI CO IA NH = 71 (292)
MI VA MO WI CO NV = 65 (286)
MI VA MO WI CO NV NM = 70 (291)
MI VA MO WI CO NV NM NH = 74 (295)
MI VA MO WI CO NV NH = 69 (290)
MI VA MO WI CO NM = 65 (286)
MI VA MO WI CO NM NH = 69 (290)
MI VA MO WI CO NH = 64 (285)
MI VA MO WI IA = 58 (279)
MI VA MO WI IA NV = 63 (284)
MI VA MO WI IA NV NM = 68 (289)
MI VA MO WI IA NV NM NH = 72 (293)
MI VA MO WI IA NV NH = 67 (288)
MI VA MO WI IA NM = 63 (284)
MI VA MO WI IA NM NH = 67 (288)
MI VA MO WI IA NH = 62 (283)
MI VA MO WI NV = 56 (277)
MI VA MO WI NV NM = 61 (282)
MI VA MO WI NV NM NH = 65 (286)
MI VA MO WI NV NH = 60 (281)
MI VA MO WI NM = 56 (277)
MI VA MO WI NM NH = 60 (281)
MI VA MO WI NH = 55 (276)
MI VA MO CO = 50 (271)
MI VA MO CO IA = 57 (278)
MI VA MO CO IA NV = 62 (283)
MI VA MO CO IA NV NM = 67 (288)
MI VA MO CO IA NV NM NH = 71 (292)
MI VA MO CO IA NV NH = 66 (287)
MI VA MO CO IA NM = 62 (283)
MI VA MO CO IA NM NH = 66 (287)
MI VA MO CO IA NH = 61 (282)
MI VA MO CO NV = 55 (276)
MI VA MO CO NV NM = 60 (281)
MI VA MO CO NV NM NH = 64 (285)
MI VA MO CO NV NH = 59 (280)
MI VA MO CO NM = 55 (276)
MI VA MO CO NM NH = 59 (280)
MI VA MO CO NH = 54 (275)
MI VA MO IA NV = 53 (274)
MI VA MO IA NV NM = 58 (279)
MI VA MO IA NV NM NH = 62 (283)
MI VA MO IA NV NH = 57 (278)
MI VA MO IA NM = 53 (274)
MI VA MO IA NM NH = 57 (278)
MI VA MO IA NH = 52 (273)
MI VA MO NV NM = 51 (272)
MI VA MO NV NM NH = 55 (276)
MI VA MO NV NH = 50 (271)
MI VA MO NM NH = 50 (271)
MI VA WI CO = 49 (270)
MI VA WI CO IA = 56 (277)
MI VA WI CO IA NV = 61 (282)
MI VA WI CO IA NV NM = 66 (287)
MI VA WI CO IA NV NM NH = 70 (291)
MI VA WI CO IA NV NH = 65 (286)
MI VA WI CO IA NM = 61 (282)
MI VA WI CO IA NM NH = 65 (286)
MI VA WI CO IA NH = 60 (281)
MI VA WI CO NV = 54 (275)
MI VA WI CO NV NM = 59 (280)
MI VA WI CO NV NM NH = 63 (284)
MI VA WI CO NV NH = 58 (279)
MI VA WI CO NM = 54 (275)
MI VA WI CO NM NH = 58 (279)
MI VA WI CO NH = 53 (274)
MI VA WI IA NV = 52 (273)
MI VA WI IA NV NM = 57 (278)
MI VA WI IA NV NM NH = 61 (282)
MI VA WI IA NV NH = 56 (277)
MI VA WI IA NM = 52 (273)
MI VA WI IA NM NH = 56 (277)
MI VA WI IA NH = 51 (272)
MI VA WI NV NM = 50 (271)
MI VA WI NV NM NH = 54 (275)
MI VA WI NV NH = 49 (270)
MI VA WI NM NH = 49 (270)
MI VA CO IA NV = 51 (272)
MI VA CO IA NV NM = 56 (277)
MI VA CO IA NV NM NH = 60 (281)
MI VA CO IA NV NH = 55 (276)
MI VA CO IA NM = 51 (272)
MI VA CO IA NM NH = 55 (276)
MI VA CO IA NH = 50 (271)
MI VA CO NV NM = 49 (270)
MI VA CO NV NM NH = 53 (274)
MI VA IA NV NM NH = 51 (272)
MI MO WI CO IA = 54 (275)
MI MO WI CO IA NV = 59 (280)
MI MO WI CO IA NV NM = 64 (285)
MI MO WI CO IA NV NM NH = 68 (289)
MI MO WI CO IA NV NH = 63 (284)
MI MO WI CO IA NM = 59 (280)
MI MO WI CO IA NM NH = 63 (284)
MI MO WI CO IA NH = 58 (279)
MI MO WI CO NV = 52 (273)
MI MO WI CO NV NM = 57 (278)
MI MO WI CO NV NM NH = 61 (282)
MI MO WI CO NV NH = 56 (277)
MI MO WI CO NM = 52 (273)
MI MO WI CO NM NH = 56 (277)
MI MO WI CO NH = 51 (272)
MI MO WI IA NV = 50 (271)
MI MO WI IA NV NM = 55 (276)
MI MO WI IA NV NM NH = 59 (280)
MI MO WI IA NV NH = 54 (275)
MI MO WI IA NM = 50 (271)
MI MO WI IA NM NH = 54 (275)
MI MO WI IA NH = 49 (270)
MI MO WI NV NM NH = 52 (273)
MI MO CO IA NV = 49 (270)
MI MO CO IA NV NM = 54 (275)
MI MO CO IA NV NM NH = 58 (279)
MI MO CO IA NV NH = 53 (274)
MI MO CO IA NM = 49 (270)
MI MO CO IA NM NH = 53 (274)
MI MO CO NV NM NH = 51 (272)
MI MO IA NV NM NH = 49 (270)
MI WI CO IA NV NM = 53 (274)
MI WI CO IA NV NM NH = 57 (278)
MI WI CO IA NV NH = 52 (273)
MI WI CO IA NM NH = 52 (273)
MI WI CO NV NM NH = 50 (271)
VA MO WI CO IA = 50 (271)
VA MO WI CO IA NV = 55 (276)
VA MO WI CO IA NV NM = 60 (281)
VA MO WI CO IA NV NM NH = 64 (285)
VA MO WI CO IA NV NH = 59 (280)
VA MO WI CO IA NM = 55 (276)
VA MO WI CO IA NM NH = 59 (280)
VA MO WI CO IA NH = 54 (275)
VA MO WI CO NV NM = 53 (274)
VA MO WI CO NV NM NH = 57 (278)
VA MO WI CO NV NH = 52 (273)
VA MO WI CO NM NH = 52 (273)
VA MO WI IA NV NM = 51 (272)
VA MO WI IA NV NM NH = 55 (276)
VA MO WI IA NV NH = 50 (271)
VA MO WI IA NM NH = 50 (271)
VA MO CO IA NV NM = 50 (271)
VA MO CO IA NV NM NH = 54 (275)
VA MO CO IA NV NH = 49 (270)
VA MO CO IA NM NH = 49 (270)
VA WI CO IA NV NM = 49 (270)
VA WI CO IA NV NM NH = 53 (274)
MO WI CO IA NV NM NH = 51 (272)
555 solutions

I don't think those probabilities are meaningful i...

2008-06-12T08:10:00.000-04:00

I don't think those probabilities are meaningful in any sense. Those states are simply the ones with the most EV's, with the exclusion of VA for some reason -- but some reason that is entirely number theoretic, not political. One must keep in mind that the "without any excess" constraint is completely artificial; in real life, nothing prevents more states going to Obama than he needs.