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"Recall that" [if one can pardon that expression] the Constitution of the United States provides that

(1) the president is elected by a college of electors, and that

(2) there are as many of those from each state as there are senators and representatives in Congress, and that

(3) there are two senators from each state and a number of representatives from each state approximately proportional to the state's population, and that

(4) the legislature in each state decides how the electors are chosen.

All but two of the 50 states give all of their seats in the electoral college to the candidate winning a majority of the votes in that state. The other two, Maine and Nebraska, elect one elector in each congressional constituency (or "district") separately and the other two electors are chosen by a vote of the people of the whole state.

The legislature of Maryland has passed a law saying all of its electors will be of the party that wins a majority of the popular vote across the whole country, provided a specified number of other states pass the same law. This law is supported by Democrats.

Now in one or more states, Republicans in the legislature have introduced bills to adopt the system used in Maine and Nebraska.

It seems to me that the Maryland bill goes all the way in a certain direction, but this last noted bill goes only part-way in the same direction; it's the same thing but less extreme. They're both moving in the direction of making the electoral college vote more likely to agree with the popular vote, but the Republican bill doesn't go as far.

But some Democrats have bitterly accused the authors of the Republican bill of trying to "rig" the electoral college's vote. I haven't seen any specificity about their rationale.

Is there some mathematical reason to view the Republican bill as other than something between the current system and the system proposed by the Maryland legistlature?

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Nice question! I'm not at all up to par in terms of politics, so I look forward to reading some knowledgeable answers. –  Clayton Mar 22 '13 at 18:31
    
@Clayton : Thank you. –  Michael Hardy Mar 22 '13 at 18:35
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BTW, the term "electoral college" is unofficial; it is found nowhere in the Constitution. It is imported from Germany, where the Latin phrase "collegium electorum" was used in the time of the First Reich to refer to the body of electors who nominally chose the king of Germany. Membership in the German electoral college was hereditary. –  Michael Hardy Mar 22 '13 at 18:40
    
For a few minutes my "reputation" was 44444. This question undid that. The charms of numerology....... –  Michael Hardy Mar 22 '13 at 18:41
    
Mathematically, the Republicans could potentially gain more votes. Take a look at Ohio's congressional districts, they're mostly Red, who did Ohio's electoral votes go to? Obama. Where is/has it been mostly blue? Around major cities, which is common. Similar conclusions can be drawn from other swing states. Furthermore, congressional boundaries aren't permanent, it's possible for either side to redraw them in their favor. –  Tony Mar 22 '13 at 18:56
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Here's a fun mathematical way to look at it:

Assume that sufficient states pass a similar bill to what Maryland Democrats support. Consider voting to be a point process in a region defined by the boundaries of the United States.

The Democratic Party's bill links the entire state's electoral votes to the global process intensity of the entire country.

The Republican Party's bill links it only to a local neighborhood.

How does this differ?

Well, if the voting process was truly random, and hence Poisson, then the Ripley's K-Function would just be $\pi r^2$ in any $r$-neighborhood in Maryland.

But, experience shows us that votes are non-uniformly distributed. They look more like a doubly-stochastic process.

Therefore, if you consider the point process to be an indicator function on a republican vote (so a vote for a republican returns 1, and a vote otherwise returns 0), then in a locally-Republican region, the K-function will be greater than $\pi r^2$.

Thus, in a sense, if Maryland is more heavily Republican, then the bill skews the electoral votes to the Republican side.

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The Maryland law is an attempt, proposed in other states, to get rid of the electoral college in a way that does not require a constitutional amendment. If passed in all the states, or in states that add to 270 electoral votes, it would do that effectively.

Based on recent voting patterns, if all the states passed the Maine/Nebraska law it seems the election would be more likely to go Republican. In 2012, the popular vote split 51.1-47.2 and we might guess that the congressional districts would split fairly evenly as well. The Democrats carried 26 states plus DC to 24 for the Republicans. The actual electoral vote count was 332-206, a substantial victory. Under the Maine/Nebraska law we might imagine it would have given the Democrats 52% of the congressional districts for a 281-257 win. In a close election you would expect the Republicans to win more than half the states, so this law would be to their advantage.

The real benefit to a party in passing the Maine/Nebraska law is if they pass it in a state that votes for the other party in the presidential election. As Democratic as California is, I would guess (can't find the map) the Republicans would have gotten about 18 of the 55 electoral votes under that law. This law has big appeal if the presidential vote in a state splits from the local government.

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Republican legislators who want to split state electoral votes in states that have recently voted Democratic in presidential elections, do not want to split electoral votes in states that recently voted Republican in presidential elections.

Dividing more states’ electoral votes by congressional district winners would magnify the worst features of the Electoral College system.

If the district approach were used nationally, it would be less fair and less accurately reflect the will of the people than the current system. In 2004, Bush won 50.7% of the popular vote, but 59% of the districts. Although Bush lost the national popular vote in 2000, he won 55% of the country's congressional districts.

The district approach would not provide incentive for presidential candidates to campaign in a particular state or focus the candidates' attention to issues of concern to the state. With the 48 state-by-state winner-take-all laws (whether applied to either districts or states), candidates have no reason to campaign in districts or states where they are comfortably ahead or hopelessly behind. Nationwide, there are now only 35 "battleground" districts that were competitive in the 2012 presidential election. With the present deplorable 48 state-level winner-take-all system, 80% of the states (including California and Texas) are ignored in presidential elections; however, 92% of the nation's congressional districts would be ignored if a district-level winner-take-all system were used nationally.

Awarding electoral votes by congressional district could result in third party candidates winning electoral votes that would deny either major party candidate the necessary majority vote of electors and throw the process into Congress to decide.

Because there are generally more close votes on district levels than states as whole, district elections increase the opportunity for error. The larger the voting base, the less opportunity there is for an especially close vote.

Also, a second-place candidate could still win the White House without winning the national popular vote.

A national popular vote is the way to make every person's vote equal and matter to their candidate because it guarantees that the candidate who gets the most votes in all 50 states and DC becomes President.

Obvious partisan machinations by Republicans now should add support for the National Popular Vote movement. If the party in control in each state is tempted every 2, 4, or 10 years (post-census) to consider rewriting election laws and redistrict with an eye to the likely politically beneficial effects for their party in the next presidential election, then the National Popular Vote system, in which all voters across the country are guaranteed to be politically relevant and treated equally, is needed now more than ever.

Maine and Nebraska voters support a national popular vote.

A survey of Maine voters showed 77% overall support for a national popular vote for President. In a follow-up question presenting a three-way choice among various methods of awarding Maine’s electoral votes, * 71% favored a national popular vote; * 21% favored Maine’s current system of awarding its electoral votes by congressional district; and * 8% favored the statewide winner-take-all system (i.e., awarding all of Maine’s electoral votes to the candidate who receives the most votes statewide).


A survey of Nebraska voters showed 74% overall support for a national popular vote for President. In a follow-up question presenting a three-way choice among various methods of awarding Nebraska’s electoral votes, * 60% favored a national popular vote; * 28% favored Nebraska’s current system of awarding its electoral votes by congressional district; and * 13% favored the statewide winner-take-all system (i.e., awarding all of Nebraska’s electoral votes to the candidate who receives the most votes statewide).

NationalPopularVote

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Mathematically, there does not appear to be any reason for the Republican-supported bill. The reason these bills have been adopted & proposed is based in how Congressional seats are selected. Each state, of course has two Senators. Since the ratification of the Seventeenth Amendment (1913), these Senators have been directly elected by a majority vote of the people of the respective state.

The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote. The electors in each State shall have the qualifications requisite for electors of the most numerous branch of the State legislatures.

So having two electors elected statewide by a majority vote is basically mirroring the election of the Congressional offices those electors "correspond" to. As for Representatives, each Representative in the U.S. House is elected directly by the people of their district. In the two states you mentioned (Maine and Nebraska), again, the electors are elected in a way that mimicks the way the corresponding Congressional members are elected.

A further discussion of the failings and benefits of the "Electoral College" is not on-topic for this site, but you can read here for a overview why is it beneficial and the logic behind its initial adoption.

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This answer doesn't address the question. The question was whether there is a mathematical reason to view the Republican bill as something other than something BETWEEN the winner-take-all system and the Maryland bill. –  Michael Hardy Mar 22 '13 at 19:16
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