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The Braess Paradox: Choice as Famine

A friend of mine who chiseled his own undergraduate curriculum at UCLA is invaluable when it comes to getting an opinion on city planning and transportation outside of the very large echo chamber that is the urbanist blogosphere. He sent me an interesting thread from Quora, the crowd sourced question-and-answer forum like Yahoo! Answers if it was made up of mostly smart people and a few PhDs, where the topic was on transportation efficiency: If you replaced 2 train tracks with a dedicated 2 lane road and ran passenger buses would it be more efficient? It’s a question that isn’t all that rare anymore with Bus Rapid Transit emerging as a low cost alternative to light rail in cities through South America and Asia; shelling out hundreds of millions of dollars to dig out new tunnels and install what amounts to be one of the more complex feats of human engineering shouldn’t be a priority for emerging economies.

The top answer on this Quora thread (again, it sounds like Yahoo! Answers but I promise it isn’t) comes from a guy named Amar Prabhu who posted a detailed economic model of transportation modal choice based on efficiency ratings (passenger load, CO2 emissions, average speed, etc.) complete with caveats and assumptions. I mean he pared down the analysis so it didn’t turn into a dissertation but, Christ, this is on a glorified knowledge forum so apparently there’s more than three dozen people actually interested in transportation that don’t hold professorships after all. I won’t go into Prabhu’s analysis (you should read it yourself) but his conclusion is that in the very short term BRT is more efficient but after three or four years a metro system becomes the better choice. Prabhu openly admits to flaws in his analysis especially on the human and policy side which are inherently tougher to model from an empirical perspective, but his number crunching is right on even if I choose to disagree with it.

As a follow up to this Quora thread, my friend sent me a Wikipedia entry on something called Braess’ Paradox (a large part of his independent curriculum was advanced economics) and, because I regret never dipping more than a toe into the intersection of traffic engineering and consumer economics, I got giddy just reading through the first paragraph. The problem is essentially this (and I encourage you to read the Wikipedia entry because I am likely to butcher this delivery and the functional notation): If commuters (let’s say exactly 4000 of them) are given two paths to work, A and B, where half of each route is a function of the number of commuters on the route (the 1st half of A and the 2nd of B; (Fc) = C/100 where C is the number of commuters) and the opposing halves have constant travel times (45 minutes in this example) then the drivers will logically split into two evenly weighted groups reducing the total travel time to an efficient equilibrium. However, if you provide the commuters with a transfer point at the halfway mark of their journeys and the transfer time is effectively 0, commuters will always choose the selfish option: take the 1st half of Route A (40 minutes with 4000 commuters) and the 2nd half of Route B (ditto) which gives us an 80 minute commute.

Easy enough right? Unfortunately these commuters have become lobotomized by choice. If you evenly split the groups into groups of 2000 like we did before the path between A and B was built then the travel times for each group would be 65 minutes; 20 minutes on the function-based halves and 45 minutes on the constant ones. Instead the commuters are choosing to reduce their travel times by five minutes by all traveling on the same route on either side of the halfway point but increasing their overall travel times by 15 minutes because of the existence of that transfer point.

500px Braess paradox road example The Braess Paradox: Choice as Famine

I’ll give everyone a chance to consider their arguments against this sort of choice paradox (here’s some starting points: “this only applies in very limited circumstances,” this is true because you have to have a population of commuters that makes both ends of the equation work which is why this is an elegant theory and not an easily applicable policy; “this applies to road choice rather than modal choice,” again, true, but on routes where two modes of transit overlap you could apply the same theoretical rigor.) but please remember that this is a vein of economics with a lot of history in transportation planning and that most of us are idiotic creatures of habit when it comes to route choice so the likelihood that we would take an 80 minute commuter over a 65 minute one because we “saved five minutes” each leg is not small.

 The Braess Paradox: Choice as Famine

It’s also something not uncommon in real world planning: commuters (especially drivers) are constantly choosing roads and highways that may have an apparent rather than real impact which is why you may see some deserted stretches of arterials that could potentially redistribute travelers efficiently. Other issues come into play when you’re discussing real world transportation issues (latent/induced demand associated with new lane construction is probably the biggest) but the Braess paradox is a novel way to look at commuter psychology.

It’s also a potential argument for more robust state-sponsored transportation systems (I’ll have to give a citation to my friend for raising that theory) because in a typical economic system choice leads to a higher performing equilibrium. If each set of commuters has two extremely well funded and maintained routes to work then there’s a higher likelihood there would be no funneling of actors from A to B and you’d reach the more stable inflection point where everyone’s travel times are reduced to a minimum. Don’t you love reading about economic paradoxes on Fridays?

 

Finding a Break Point for Gasoline Prices

I’m a little late on the gas price bandwagon with analysis and meta-analysis already covering most of the major transportation and urbanism blogs across the domestic blogosphere. Everyone agrees on a few things: that the public is misguided in thinking that President Obama can influence gas prices in any significant way, that gas prices were artificially low for at least two decades hence, that America still has some of the cheapest gas in the world, and that we are beginning to see the effects of so-called Peak Oil. High concepts are relatively easy to reach consensus on, but what is significantly less clear is what these climbing prices means for the average family.

gas pump Finding a Break Point for Gasoline Prices

Gas spikes typically mean fewer miles spent on the road for obvious reasons. And given the stubborn economic malaise in this country there is worry that upward pressure at the pump in 2011 means something different than it did a decade ago and that (gasp) high gas prices could even put the brakes on a recovering economy. Unfortunately most of the panic is based on heuristic evidence which leaves little to no room in the debate for hard statistics on what the most recent crisis means empirically for families, but thanks to the pollsters at Gallup we now have a decent guess.

According to a Gallup survey published on March 8th, the breaking point for most American families lies somewhere between $5.30 and $5.35—a full $1.50 more than the average American is paying for one gallon of regular unleaded and $1.20 more than those filling up their Benzs and Beamers with premium based on today’s AAA Fuel Gauge Report, a daily report based on up to 100,000 filling station prices. Even more telling is that only 17% of Americans would have to alter their spending habits at gas prices under $4.00 (current average price of regular unleaded: $3.846.)

Gallup Poll Finding a Break Point for Gasoline Prices

The statistics aren’t perfect, of course. States that have low state gas taxes like Georgia and Missouri (as well as Alaska which doesn’t collect one at all) are affected less by real prices of gasoline than states like California and New York, where state gas taxes are higher and demand is extremely high (Californians are paying an average of $4.348 today). Low density states like California, Texas, and Oklahoma are also faced with little recourse to driving nearly everywhere, whereas populations in infrastructure heavy states like New Jersey are able to simply shift their mode of transportation given a shift in pricing. Gas price impacts are understandably lumpy.

Still, with only two states at within one dollar of Gallup’s breakpoint (Hawaii joins California, though we should really consider Hawaii as an exception for obvious geographical reasons) is there much of a reason to panic? Not particularly, and for many progressive transportation advocates this should be viewed as a free look into the politics of raising gas prices whether it’s a “natural” market phenomenon like this or a potentially artificial one like a gas tax hike. Unfortunately the violent outcry against high gas prices and the absolute inability for a majority of Americans to understand exactly what drives gas prices to do what they do even though they think they do (phew) has shown that there is no taste for paying fair market price for a gallon of fuel (and it should be added that this author doesn’t pretend to fully understand the lever-pulling and politicking that goes into gasoline prices). Gasoline consumers (much like public transit consumers in an odd twist of infrastructure fate) would rather not face the complex economic realities of their chosen good—that it is much more complicated than point-t0-point navigation and that price is not a reflection of mood or climate but of competing realities.

(Aside: the environmental argument doesn’t even merit consideration here because it’s almost superfluous. We are consuming a finite resource that has eluded optimal management practices for everyone outside of a few OPEC countries who shrewdly know how to control their taps; it’s market heresy to want to pay a semi-fixed price [<$3.00/gal let's say] when we are sliding down the supply line steadily yet many who embrace that brand of economics don’t see it that way. Untapped domestic petroleum sources buy us another 15 years, a middling piece of temporal real estate geopolitically speaking.)

So we’re sort of stuck. Gas prices will continue to oscillate with the seasons and panic will undoubtedly tag along. We will continue to care and then, somehow, not care until we care again. It’s just gas, after all, and we can always get more.