If you’re havin’ electoral problems I feel bad for you son, I got 538 problems but partisan bias ain’t one

As Andrew Thomas, Gary King, Jonathan Katz, and I discussed in our recently published article (see also discussion here), the electoral college has had little partisan bias in recent decades. By this we mean that, by our calculations (details below), the percentage of the two-party vote needed by the Republican or Democratic candidate to have a 50/50 chance of winning in the electoral college is close to 50%.

In the wake of the 2012 election there has been some talk of an electoral college lock benefit for Obama (see, for example, this article by Nate Cohn). After looking at the state-by-state results carefully, we agree: our retrospective estimate is that Romney needed about 50.5% of the national two-party vote to have had a 50/50 chance of winning in the electoral college.

This is a bias, for sure, but a small bias. Enough to have made a difference in 2000 (when Al Gore received 50.3% of the two-party vote) but not 2004 (when George W. Bush received 51.2%).

In contrast, the bias that would ensue if the electoral vote were conducted via congressional districts—-that would be huge.

And, again, there’s nothing particularly special about 2012. In most of the elections of the past several decades (only the blowouts of 1964 and 1984 excepted), the partisan bias of the electoral college has been small but the partisan bias of a CD-based system would’ve been huge.

This is not to say the electoral college is perfect—-like many others, I find the focus on “battleground states” to be distorting, and I’d prefer a national popular vote system—-but the problems of the electoral college aren’t really one of partisan bias. And we shouldn’t let the occasional and small partisan bias of the existing electoral college serve as any sort of excuse for instituting changes which would increase bias to a whole new level.

My quick calculation

I started by applying a uniform partisan swing to the state-by-state vote, increasing Romney’s share until he reached the magic 270 electoral votes. He would need 51.2% of the popular vote.

But that calculation’s not quite right. In a hypothetical replicated election, the state votes would not be swung exactly uniformly. You can see my 1994 paper with King for details, but the basic idea is to add noise at the state level.

To keep things simple, I redid the what-would-Romney-need-to-get-270 calculation using expected electoral votes, after adding independent randomly distributed noise with standard deviation sigma to the state-level vote totals. This isn’t quite right (again, see the 1994 paper for details) but it should be close enough.

With sigma = 1% or 2%, Romney would need 50.7% of the two-party vote to have a 50/50 chance of winning at least half the electoral votes.

With sigma = 3%, Romney would need 50.6% of the vote. With sigma = 4%, he’d need 50.5%. With sigma = 5%, he’d need 50.4%.

Overall, 50.5% seems to me a reasonable summary. Again, a bias of zero would be preferable, and, like Nate Cohn, I’d be happy for this to be used as an argument to move toward a national popular vote system, but it’s much smaller than the bias associated with the count-the-winners-of-the-congressional-districts system.

10 Responses to If you’re havin’ electoral problems I feel bad for you son, I got 538 problems but partisan bias ain’t one

  1. oldgulph February 1, 2013 at 4:20 pm #

    The National Popular Vote bill would guarantee the Presidency to the candidate who receives the most popular votes in all 50 states (and DC).

    Every vote, everywhere, would be politically relevant and equal in presidential elections. No more distorting and divisive red and blue state maps. There would no longer be a handful of ‘battleground’ states where voters and policies are more important than those of the voters in 80% of the states that now are just ‘spectators’ and ignored after the conventions.

    When the bill is enacted by states with a majority of the electoral votes– enough electoral votes to elect a President (270 of 538), all the electoral votes from the enacting states would be awarded to the presidential candidate who receives the most popular votes in all 50 states and DC.

    The presidential election system that we have today was not designed, anticipated, or favored by the Founding Fathers but, instead, is the product of decades of evolutionary change precipitated by the emergence of political parties and enactment by 48 states of winner-take-all laws, not mentioned, much less endorsed, in the Constitution.

    The bill uses the power given to each state by the Founding Fathers in the Constitution to change how they award their electoral votes for President. Historically, virtually all of the major changes in the method of electing the President, including ending the requirement that only men who owned substantial property could vote and 48 current state-by-state winner-take-all laws, have come about by state legislative action.

    In Gallup polls since 1944, only about 20% of the public has supported the current system of awarding all of a state’s electoral votes to the presidential candidate who receives the most votes in each separate state (with about 70% opposed and about 10% undecided). Support for a national popular vote is strong among Republicans, Democrats, and Independent voters, as well as every demographic group in virtually every state surveyed in recent polls in recent closely divided Battleground states: CO – 68%, FL – 78%, IA 75%, MI – 73%, MO – 70%, NH – 69%, NV – 72%, NM– 76%, NC – 74%, OH – 70%, PA – 78%, VA – 74%, and WI – 71%; in Small states (3 to 5 electoral votes): AK – 70%, DC – 76%, DE – 75%, ID – 77%, ME – 77%, MT – 72%, NE 74%, NH – 69%, NV – 72%, NM – 76%, OK – 81%, RI – 74%, SD – 71%, UT – 70%, VT – 75%, WV – 81%, and WY – 69%; in Southern and Border states: AR – 80%, KY- 80%, MS – 77%, MO – 70%, NC – 74%, OK – 81%, SC – 71%, TN – 83%, VA – 74%, and WV – 81%; and in other states polled: AZ – 67%, CA – 70%, CT – 74%, MA – 73%, MN – 75%, NY – 79%, OR – 76%, and WA – 77%. Americans believe that the candidate who receives the most votes should win.

    The bill has passed 31 state legislative chambers in 21 states with 243 electoral votes. The bill has been enacted by 9 jurisdictions with 132 electoral votes – 49% of the 270 necessary to go into effect.

    Follow National Popular Vote on Facebook via NationalPopularVoteInc

  2. Levine February 1, 2013 at 6:46 pm #

    70% of the American Electorate did NOT vote for OBAMA in November 2012. A rather sad reality of the beloved “popular vote”.

    That’s typical of Presidential elections. It should give one great pause when “optimizing” the desired election process.

    Think about what you really care about in the concept of a U.S. Presidential election. What is the ultimate objective for the American citizenry in all this, and for you personally ?

    Process should be secondary to the primary objective. Most have lost sight of that objective, if ever noticed at all.

    • Andrew Gelman February 1, 2013 at 10:00 pm #


  3. Nate Cohn February 1, 2013 at 7:02 pm #

    Three things:
    1) It’s not remotely accurate to suggest that I advanced a case for a Democratic EC “lock,” and it’s equally ridiculous to imply I was drawing an equivalence between the advantage Democrats currently posses under the Electoral College and the one Republicans might hold if states apportioned their electoral votes by congressional district. The latter suggestion is so preposterous that you must be arguing against a straw person, even though it sometimes reads as though you’ve attributed that position to myself. After all, the admittedly simple (but hardly useless) uniform swing would show a Democratic disadvantage under the CD system of much more than twice the size as the one that the GOP faces under the WTA system.
    2) At a broad level, I don’t see why you’ve disagreed with my argument at all, except in so far as the piece mentioned the uniform swing. Whether Romney might have needed 51.2 or 50.5 percent (or perhaps 50.7, since 50.5 seemed pretty arbitrary) of the popular vote is a reasonable discussion (more on this later), but the GOP faces a deficit in the Electoral College under either calculation, and that was the extent of my case.
    In so far as the uniform swing might be a point of disagreement, my piece used the uniform swing for illustrative purposes, not to identify the GOP’s victory threshold with any precision. In fact, the piece acknowledges several of sources of uncertainty–mainly in terms of coalitional changes cutting across demographic lines, like concentrated GOP gains among groups that aren’t distributed evenly across the electoral map–that could potentially attenuate or exacerbate the GOP’s Electoral College disadvantage. Realistically, it won’t take 51.2 percent of the two-party vote for the next Republican to claim the presidency, since they’ll be wise enough to aim for gains among the demographic groups critical to pivotal states like Colorado. The GOP’s quick shift on immigration reform is a helpful example.
    3) Although I don’t think you’ve disagreed with much of what I actually argued in my piece, I have questions about your particular method for estimating the bias of the EC.
    If the “uniform swing” suffers because it doesn’t account for uncertainty, then “independent randomly distributed noise” is also inappropriate for describing the dependent and …unrandom(?) state-level shifts in a diverse country.
    Historically, changes in the composition of the two party coalitions occur among particular groups or regions—like Bush’s gains among white conservatives in Appalachia, Nixon’s in the South, or Obama’s in well-educated and diverse communities. A uniform swing wouldn’t have anticipated George W. Bush’s comfortable wins in Louisiana, Arkansas, and West Virginia, or Obama’s wins in Virginia, North Carolina, or Colorado.
    As a result, the uniform swing is actually a relatively ineffective tool for imaging the winning map for the next Republican president, even if it indicates that the GOP will need to make disproportionately large gains in several Obama-leaning states. But for that same reason, “random variance” isn’t especially useful, either. It does get at the uncertainty, but the variance isn’t random.
    Building in something like 4 percentage points worth of random variance strikes me as wildly overdone. Demographically similar states seem to move in unison: Pennsylvania always manages to vote a few points to the left of Ohio or Virginia to the left of North Carolina, which wouldn’t be so consistent if the SD of variance was 4 pts. To the extent that there is variance in the positioning of demographically similar states, it still might not be random. Obama’s poor performance in Pennsylvania compared to Ohio, for instance, is easily attributed to Obama’s weakness in Appalachia, which is a far greater part of the state. I admit the following example is a little unfair, but an unpublished effort to predict the state-by-state ’12 results based on the ’08 results and 9 demographic or empirical variables was quite successful. Once Obama’s 3.9-point PV margin was specified, the median error among the battleground states was approximately .5 points, with all 12 contested states falling within +/-1.2 points of their eventual result. Given that the model was relatively rudimentary, one wonders how much of the outstanding error was truly random, or due to unspecified variables, like Appalachia, Mormons, or the varied investment of the two campaigns (the two errors surpassing 1 point were Nevada and Pennsylvania). While there may be a modest amount of true “randomness,” it’s much smaller than the observed state-by-state variance.
    Given the non-random character of state by state variance and the importance of demographic variables, it may not be possible to accurately estimate the scale of the GOP’s EC disadvantage. A more accurate approach would to reduce the amount of variance due to randomness and simulate plausible permutations of coaliational changes. That’s admittedly quite subjective, but it’s what I alluded to in my piece. It is worth observing that a decline in black turnout and support for the next Democratic candidate could easily produce a close popular vote without nearly enough GOP gains in Colorado or Pennsylvania to win the presidency. Obviously holding everything else constant is ridiculous, but it hints at the appropriate approach: less variance due to uncertainty, more simulation of different permutations of gains among different permutations of demographic gropus, and an eye for which types of gains are most plausible.
    Just how large would the GOP’s Electoral College disadvantage be? I’m not sure. I didn’t claim it would be of any particular size.

    • Andrew Gelman February 1, 2013 at 9:58 pm #


      Your point 3 above is correct. I do not disagree with anything you wrote, and I apologize if my original phrasing implied otherwise. I have rewritten the above post to clarify (I hope). At no point was I intending to dispute your article; I linked to it because it was a thoughtful and sensible discussion of the issue.

      My main point was that the bias of a CD-based system would be huge. In the above post, I gave my best estimate of the partisan bias of the electoral college, but I agree with you that any consideration of hypothetical elections depends on assumptions. I made some simple assumptions; others are possible. Also, that’s one reason I gave results for 1% or 2% of random error; in those cases, Romney’s magic number would be 50.7% of the two-party vote.

      • Nate Cohn February 4, 2013 at 11:40 am #

        I appreciate the revision

  4. b-psycho February 1, 2013 at 8:26 pm #

    The congressional district form of allocation would make it so, barring unforeseen shifts in the electorate on a district by district basis and/or high rates of ticket splitting, the person most likely to win the presidency would be the one with the majority in the House. It’d effectively turn it into a parliament-ish position.

    Which is highly ironic considering which party is advocating for it…

  5. DavidT February 1, 2013 at 9:48 pm #

    FWIW, of the last fourteen presidential elections, three have been three where the winning candidate got less than 50.5% of the two-party vote: 1960, 1968, and 2000. So while that is not particularly common, it is not freakishly rare either.

    • Andrew Gelman February 1, 2013 at 9:53 pm #


      I agree. As noted, I’d prefer a system with zero partisan bias. I just wanted to emphasize that the small and fluctuating bias of the electoral college is minor compared to the huge bias that would occur under the congressional district system.

  6. John Mashey February 4, 2013 at 10:21 pm #

    Ignoring all the statistics, to me the high-order bit is simple:
    Unlike either:
    1) The current Electoral College OR
    2) A national popular vote

    A CD-based system lets a party in power in a state when it’s time to redistrict, rearrange districts in such a way as to disenfranchise as many people as possible of the other party, in states where the elected politicians get to do that, i.e., extends the power of the gerrymander to the Presidential election.