energy prices

 A week or two ago, Texas experienced some unusual weather which, by means of a couple different mechanisms, reduced the supply of electricity while increasing its demand.  The wholesale price of electricity shot up to $9 per kWh, where it is capped, and many people had their power shut off altogether as they were sacrificed to preserve electricity for priority customers (e.g. hospitals).  Other people kept receiving power; some of them have retail providers who pass along the wholesale price of the power, and many of them are now seeing very large power bills, some over $10,000.

There are a few things that I've been thinking about related to this.

• If you were to draw an actual "marginal benefit" curve, based on some plausible measure of customers' own valuation of marginal units of power, it doesn't seem to me like it would be as inelastic as these price dynamics imply. My impression is that a lot of the people who were shut off would have been unwilling to pay $10,000 to instead have power through the week, and especially that, given the choice between paying $10,000 to use that much power or $5,000 to have half as much, they would have opted for the latter. Perhaps I'm simply wrong here; suppose I'm not.
  • How well were the customers paying variable rates able to track and control their use of electricity? Presumably they have some kind of smart meter that at least knows when they used power; are their meters able to communicate the price in real time, maybe shut off appliances or change thermostats? (Did these people take steps to lower thermostats themselves?)
  • What is it about the way the market is structured that caused the price to get well ahead of marginal benefit (assuming, again, that that's what happened)? Perhaps if more consumers had been on variable-rate plans the system would have been more robust. Any power that was used that was not worth the price to the customers was presumably used either in ignorance of the price or under an arrangement in which the person deciding to use the power was insulated from the cost.
• The supply side, on the other hand, does seem really to have been quite inelastic; the marginal cost, I'm guessing, was well under $1 per kWh up to a very high percentage of the amount actually being supplied, with a sharp upturn at that point. Classical Marshallian welfare analysis suggests that, in such a context, "producer" surplus will be very high. In a rational expectations model with free entry, sellers would expect these kinds of episodes and the surplus would be used to cover fixed costs and/or induce entry. In the real world, it does look like a nice reward for the producers that were able to keep producing power, perhaps because they had prepared better for a situation like this, or perhaps because they were lucky. (Usually there's some of each.) I don't know whether it's likely to induce local improvements to robustness or not.
• Some of the drop in supply seems to have been that gas-fired plants weren't able to get natural gas. Few if any retail gas customers seem to have lost gas, however; it was apparently prioritized first to households, with power plants lower in priority. I have heard the word "obviously" attached to this decision, perhaps because cutting off gas to households that use gas during a cold snap would mean those houses would lose heat, yet what did happen is that many houses that use electricity for heat had their heat cut off during a cold snap. I don't know that the physics of the gas pipes would allow households to have some throttled quantity of gas, but it seems likely that some alternation — rolling gas-outs designed to provide gas to households when it's likely they're dropping below some temperature like 45 or 55 degrees, but provide some gas to the plants producing the power to heat other houses — would have been better on the whole.

Runoff voting with runoff

Voting for a single winner between two candidates is straightforward; if the candidates and voters are all to be symmetric, then asking each voter which candidate to prefer and electing the candidate with more votes is relatively[1] problem-free and is the obvious way to determine a winner.  With multiple candidates things get tricky; in particular, our usual plurality system results in "vote splitting", where the result depends as much on which candidates decide to run as it does on who the voters prefer; for example, perhaps Alice gets 40% of the vote, Bob gets 39%, and Carol gets 21%, and it may be the case that more voters preferred Bob to Alice, but some of them voted for Carol instead. 

One increasingly popular way of addressing this is with instant runoff voting; voters in Maine (and, going forward, Alaska) rank their options, indicating that one candidate is the voter's first choice, another the second choice, and so on.  When the votes are tallied, each vote is counted for the candidate ranked first, but if no candidate gets a majority, the candidate with the fewest votes is eliminated, and ballots are recounted, being credited to the highest ranked remaining candidate.  Older runoff systems in the United States ask voters to come back to vote in subsequent rounds with fewer candidates, but the instant runoff with ranked ballots can do this automatically without calling the voters back to the polls because the voters have implicitly left instructions on how they wish to vote in the runoff.

One problem with this procedure is that it can frequently eliminate popular second choices.  For example, it may be that the 40% who voted for Alice prefer Carol to Bob, and the 39% who voted for Bob prefer Carol to Alice; Carol is the top choice of fewer voters than the others, but is nobody's least favorite candidate, and in particular she would win the election if either of the other candidates dropped out.  A majority of the voters prefer Carol to Alice, and a majority prefer Carol to Bob, but Carol is dropped from the runoff, and one of candidates who she would have beat will win instead.

This is not too hard to fix with a relatively small change to the procedure: when deciding which candidate to eliminate, we look at both of the two candidates with the fewest votes, and eliminate whichever is ranked lower on more ballots.  In this case, we see that Bob and Carol have the fewest first-place votes, so one of them will be eliminated; because 61% of voters prefer Carol to Bob, we eliminate Bob.  Alice and Carol are in the runoff, where Carol wins.

Maine has published the ballots from the House of Representatives election for 2018 in its second district, and, while I have trouble figuring out exactly how the state interpreted some of the ballots, I can use them for an example.  By my count, Poliquin was the top choice of 134,358 voters, Golden of 132,145, Bond of 16,650, and Hoar of 6,996.  In Maine, this was enough to eliminate Hoar; in my system, we first compare him to Bond.  Of the ballots expressing a preference between them, there were 43,131 more ballots that had Bond ranked above Hoar than vice versa; it is only after we observe this that we eliminate Hoar.  This leaves three candidates, and we redistribute the 6,996 votes for Hoar; Poliquin now has 135,275 votes, Golden has 133,381, and Bond has 19,313.  Because Golden beats Bond by 96,458 votes when only those two candidates are considered, we eliminate Bond.  Less than 4,000 of her votes transfer to Poliquin, though; in the final round, he has 139,238 votes, while Golden has 142,664.  Golden is therefore elected.

Golden	132,145	133,381	142,664
Poliquin	134,358	135,275	139,238
Bond	16,650	19,313
Hoar	6,996

---

[1] I'm going to assume away exact ties, as I so often do.