# Curious arithmetic fact: Colorado is no bigger than New Hampshire

I’ve noticed an interesting fact about the Electoral College vote coming up in 14 months. Perhaps this observation is more appropriate for Mundane-Pointless but it does have direct bearing on the election. (I’ll guess Nate Silver figured this out long ago, but I noticed it independently and this is my show-and-tell. )

I start with the assumption that a 269-269 tie would lead to a Republican President (though perhaps a Democratic Vice Pres). Is this correct?

To present the arithmetic fact, one needs a list of swing states. The specifics of the list of swing states does not affect the interesting arithmetic fact. If you disagree that Pennsylvania or Wisconsin is a swing state, just cross it off the list – the result is the same. If you “need” to vocalize your belief that PA or WI isn’t a swing state, please start another thread. Note that for our purpose here “swing state” does not mean state likely to go either way, but means*** state likely to go either way if the election is close**.*

To prepare the list of swing states I’ve considered not just 1st statistical parameter (redness vs blueness) but 2nd parameter as well (Silver’s “elasticity”). Ohio and Florida are the biggest swing states of all, but we can ignore them for this purpose: Because if the Democrats win either of them, Democrats take the White House; all the other swing states become irrelevant. (Similarly, optimists think it’s far more likely that Democrats take North Carolina than that the GOP takes Pennsylvania, but only close elections are relevant to this type of analysis.)

Consider the seven swing states (shown with electoral votes and “point” defined below):

``````

Pennsylvania   20  (3)
Virginia       13  (2)
Wisconsin      10  (2)
Iowa            6  (1)
New Hampshire   4  (1)

``````

The electoral vote stands at 253-217 if the other 44 states split as expected. The GOP needs 16 votes from the swing states to win.

The curious arithmetic fact is that you needn’t memorize the electoral votes to see who wins when. Just the final column (3-2-2-1-1-1-1) is good enough. The GOP needs three of these “points.” (A sole exception is the unlikely Wisconsin-New Hampshire combo: 3 “points” but not quite enough for GOP victory.)

In other words, Colorado, with 9 electoral votes is no more valuable than New Hampshire with just 4 electoral votes!

Sure. I’d also point out that by your own logic, Ohio at 18 EV is just as good as Florida at 29.

The only nitpick I’d have is that at a 269-269 vote, both the VP and Pres would go to the GOP, since it’s the current Senate that would end up choosing the VP.

Where are you getting this data? The “Blue Wall”, states that the Democrats have won every year since 1988, stand at 257. It’s the Democrats who have the large advantage, needing only 13 more electoral votes to win.

IA, NH, NM each went Republican once in that span.

Well, I just didn’t solve for the cases where Florida and Ohio are in contention. When I do, I get this (states sorted roughly red to blue – please check for me):

``````

Florida        29  (5)
Ohio           18  (3)
Virginia       13  (2)
Iowa            6  (1)
New Hampshire   4  (1)
Wisconsin      10  (2)
Pennsylvania   20  (3)

``````

The GOP needs 63 EV or 11 points, when the other 42 states split as expected.
The point assignments shown do not predict all outcomes perfectly, but if you simply add a point for the GOP whenever it wins both Pennsylvania and Colorado, almost all will be right. (By far the biggest residual error left will be the Wisconsin plus New Hampshire loss already mentioned. Anyway, if the GOP wins PA, it’s almost certainly also taking OH and FL for the win, making CO irrelevant.)

None of those states are part of the “Blue Wall.”

That only gets you to 242. Adding the three I mentioned puts you at 257, so I assumed that’s what you were thinking of.

septimus is talking about a hypothetical close election in which the map is tilted red, relative to most projections–he means 253 EV for the Republican candidate.

Yes. Or look at the table in #5 to treat OH and FL as swing states.

There are three possibilities:

• Democratics win the election easily,
• Republicans win easily,
• The election is very close.

For my purpose here I can be agnostic on whether Demo landslide is much more likely than GOP landslide or not. *It’s only the elections that are very close that are relevant for worry about every last electoral vote. * (It doesn’t matter whether these cases are near the middle of the bell-curve or off to one side.) And regardless of whether you include OH, FL, PA, WI, NV in the list of swing states or not, the essential conclusion remains:

Colorado is worth only a very tiny bit more than NH.

I am failing to understand what the point of the “curious arithmetic fact” is.

Yes. IF one assumes out of the gate that the GOP candidate wins Ohio and Florida, and that North Carolina is not in play, and that they also get the other states they got before (a reasonable expectation in any election that gives them both Ohio and Florida) then they start with 253, and need some combination out of other states that are potentially flippable to get them over.

In that one hypothetical PA alone would do it (hence 3 points) or VA plus another state (hence it’s worth 2) or otherwise any reasonable combination takes three states of the ones that are imaginable to flip next as the GOP popular vote majority gets higher overall.

Does one really need points for that?

No it’s the newly elected House and Senate that vote. They take office early in January. However, in the House each state (not each representative) gets one vote, and I suspect that favors Republicans even more than the representative count does.

Out of curiosity, what is the least unlikely scenario that comes up with a 269 tie?

I can create FL, NC, WI, NH, and PA all going Red with OH, VA, IA, and CO all going Blue to get there … any other combinations?

I doubt PA would go red before all of IA, OH, VA.

FL, IA, NC, OH, WI Red and CO, NH, PA, VA Blue seems more likely. That posits an overall redward slide in the popular vote relative to 2012, with the Republican nominee holding every Romney state, and picking up two of three of the closest Obama states from that year (FL, OH), and seeing a bump in white conservative turnout in the Midwest that flips IA and WI. But NH and VA stay blue.

An electoral tie is definitely a Republican victory when the House delegations vote.

Well, yes, but only because neither are the only states. Their votes are combined with several other states. As a group, these states add up to roughly the same for each side, hence the swing states.

Curious arithmetic fact: Colorado is no bigger than New Hampshire

It seems at least mildly curious to me that Colorado with 9 EV is worth no more than NH with 4 EV – less than half Colorado’s vote weight. YMMV; Yadda yadda.

Obviously “points are not really needed”; details of the curiosity can be expressed in ordinary and elegant English; I toyed with posting both formulations, but opted toward brevity. Note that the point-count formulation is
[ul][li] very clear,[/li][li] terser and more complete than an elegant English formulation,[/li][li] easily converted to an English formulation.[/li][/ul]
I apologize for any confusion. If necessary I will post the exposition in ordinary English.

And sorry if this comes off as snarky … I do not mean to …but is sort of like saying it is curious how a a field goal and a touchdown both win a game in the last second of play for a team that is two points down.

There a two fairly well known systems for determining the power that a player has in weighted voting system. The Banzhaf power index and the Shapley–Shubik power index.

For the weighted voting system in post #1 (written [17; 20,13,10,9,6,6,4]) we can calculate each:

Banzhaf -> [17/65, 15/65, 9/65, 9/65, 5/65, 5/65, 5/65]
Shapley-Shubick -> [1908/5040, 1068/5040, 564/5040, 564/5040, 312/5040, 312/5040, 312/5040]

In both cases Colorado has the amount of “power” as Wisconsin and Iowa, Nevada, and New Hampshire are all equal and less powerful.

In fact with respect to both power indices [17; 20,13,10,9,6,6,4] is equivalent to [4; 4,3,2,2,1,1,1] and not [3; 3,2,2,1,1,1,1] as specified in the OP.

On rereading I see that the original system should be [16; 20,13,10,9,6,6,4] since the red team would prevail in the event of 269-269 tie.

In that case we have:

Banzhaf -> [14/58, 12/58, 10/58, 6/58, 6/58, 6/58, 4/58]
Shapley-Shubick -> [1776/5040, 936/5040, 768/5040, 432/5040, 432/5040, 432/5040, 264/5040]

Here we have CO, IA, NV equally powerful with a slight edge over New Hampshire.

So I’ve been thinking a little more about this. If we use the Cook Partisan Voting Index and concede everything with Republican lean to the Republicans that gets us to 253 EV.

Now if we consider only states that are even or have a 1 point Dem lean to be swing states we have CO, IA, NH, PA, and VA. In this weighted voting system ([16; 20,13,9,6,4]) CO, IA and NH all have exactly the same amount of power.

Furthermore, if we concede VA to Republicans. Then the Republicans only need 3 more EV. In this case every state we consider a swing state has equal power. So NH would be equally as important as PA here.

Right. Just look at the 2000 election. If Gore flips one single Bush state, he wins. In that vein, one could say that Alaska has exactly the same voting power as Texas!