Postdoc in Applied Category Theory

8 September, 2017

guest post by Spencer Breiner

One Year Postdoc Position at Carnegie Mellon/NIST

We are seeking an early-career researcher with a background in category theory, functional programming and/or electrical engineering for a one-year post-doctoral position supported by an Early-concept Grant (EAGER) from the NSF’s Systems Science program. The position will be managed through Carnegie Mellon University (PI: Eswaran Subrahmanian), but the position itself will be located at the US National Institute for Standards and Technology (NIST), located in Gaithersburg, Maryland outside of Washington, DC.

The project aims to develop a compositional semantics for electrical networks which is suitable for system prediction, analysis and control. This work will extend existing methods for linear circuits (featured on this blog!) to include (i) probabilistic estimates of future consumption and (ii) top-down incentives for load management. We will model a multi-layered system of such “distributed energy resources” including loads and generators (e.g., solar array vs. power plant), different types of resource aggregation (e.g., apartment to apartment building), and across several time scales. We hope to demonstrate that such a system can balance local load and generation in order to minimize expected instability at higher levels of the electrical grid.

This post is available full-time (40 hours/5 days per week) for 12 months, and can begin as early as October 1st.

For more information on this position, please contact Dr. Eswaran Subrahmanian ( or Dr. Spencer Breiner (

Wind Energy in Texas

6 November, 2016

Here’s an interesting story about the rise of wind energy in Texas:

• Richard Martin, The one and only Texas wind boom, Technology Review, 3 October 2016.

I’ll quote the start:

Rolan Petty stabbed at the dirt with a boot toe and looked up at the broiling west Texas sun. “I call it farming on faith,” he said of his unirrigated cotton farm. “You just have faith that the rain is gonna come.”

If it doesn’t come, Petty has a backup income stream: leasing fees. All around us, towering 150 feet over Petty’s combine and the scrubby-looking cotton plants in neat rows, stood a forest of wind turbines that stretched to the horizon. Petty’s land on the arid plain of west Texas lies on the edge of the vast Horse Hollow wind farm, with 430 turbines spread over 73 square miles. It was the largest wind farm in the world when it was completed, in 2006. Petty’s family leases land to Horse Hollow and another wind farm in the area, making about $7,500 a year on each of the several dozen turbines on their property. Wind power has become a big windfall for the Pettys, as it has for many landowners in Texas—allowing Rolan and his parents and three brothers to make hundreds of thousands of dollars every year whether the rains come or not. And the Petty farm is just a small player in the largest renewable-energy boom the United States has ever seen.

With nearly 18,000 megawatts of capacity, Texas, if it were a country, would be the sixth-largest generator of wind power in the world, right behind Spain. Now Texas is preparing to add several thousand megawatts more—roughly equal to the wind capacity that can be found in all of California. Most of these turbines are in west Texas, one of the most desolate and windy regions in the continental United States. Fifteen years ago, when the groundwork for this boom was being set, this area had little but cotton and grain farms, oil fields, scrub and dry riverbeds, and small towns that were mostly withering.

Today it’s a land of spindly white turbines that line the highways—and the pockets of landowners. At night, when the wind blows strongest and steadiest, if you stand out in one of the fields you can hear the great blades make a ghostly shoop-shoop sound as they turn. Wind power has brought prosperity to towns that were literally drying up less than a generation ago. “In the 2011 drought a lot of people around here would have filed for bankruptcy if not for the turbines,” said Russ Petty, one of Rolan’s brothers, who was giving me a driving tour of the property. “What it’s done is helped keep this land in the family.”

It has also shown that a big state can get a substantial amount of its power from renewable sources without significant disruptions, given the right policies and the right infrastructure investments. The U.S. Department of Energy’s 2015 report Wind Vision set a goal of getting 35 percent of all electricity in the country from wind in 2050, up from 4.5 percent today. In Texas, at times, that number has already been exceeded: on several windy days last winter, wind power briefly supplied more than 40 percent of the state’s electricity. For wind power advocates, Texas is a model for the rest of the country.

But it also reveals what wind power can’t achieve. Overall, wind still represents less than 20 percent of the state’s generation capacity—a number that dips into the low single digits on calm, hot summer days. And even with the wind power boom, the state’s total estimated carbon emissions were the highest in the nation in 2013, the most recent year for which data is available—up 5 percent from the previous year.

What’s more, the conditions that have spurred Texas’s boom may not be easily duplicated. Not only is Texas scoured by usually steady winds, but it has something most other places lack: a gigantic transmission system that was built to bring electricity from the desolate western and northern parts of the state to the big cities of the south and east, including Dallas, Austin, San Antonio, and Houston. Under a program known as Competitive Renewable Energy Zones, or CREZ, the power lines were approved in 2007 and cost nearly $7 billion to build. They have added a few dollars a month to residential electricity bills, but they now look like a far-sighted infrastructure investment that other states are unwilling or unable to make.

I drove nearly 1,200 miles, from Abilene to Amarillo and many places in between, this summer to explore the wind explosion in Texas. I wanted to understand what was driving this ongoing boom, and what the ultimate limit might be. How much wind power can the Texas grid absorb, economically and physically? And can other states, and other nations, achieve what Texas has, or are there conditions here that will be difficult or impossible to reproduce anywhere else?

Read the rest here.

Renewable Energy News

1 August, 2016

Some good news:

• Ed Crooks, Balance of power tilts from fossil fuels to renewable energy, Financial Times, 26 July 2016.

These are strange days in the energy business. Startling headlines are emerging from the sector that would have seemed impossible just a few years ago.

The Dubai Electricity and Water Authority said in May it had received bids to develop solar power projects that would deliver electricity costing less than three cents per kilowatt hour. This established a new worldwide low for the contracted cost of delivering solar power to the grid—and is priced well below the benchmark of what the emirate and other countries typically pay for electricity from coal-fired stations.

In the UK, renowned for its miserable overcast weather, solar panels contributed more power to the grid than coal plants for the month of May.

In energy-hungry Los Angeles, the electricity company AES is installing the world’s largest battery, with capacity to power hundreds of thousands of homes at times of high demand, replacing gas-fired plants which are often used at short notice to increase supply to the grid.

Trina Solar, the Chinese company that is the world’s largest solar panel manufacturer, said it had started selling in 20 new markets last year, from Poland to Mauritius and Nepal to Uruguay.


Some new energy technologies, meanwhile, are not making much progress, such as the development of power plants that capture and store the carbon dioxide they produce. It is commonly assumed among policymakers that carbon capture has become essential if humankind is to enjoy the benefits of fossil fuels while avoiding their polluting effects.

It is clear, too, that the growth of renewables and other low-carbon energy sources will not follow a straight line. Investment in “clean” energy has been faltering this year after hitting a record in 2015, according to Bloomberg New Energy Finance. For the first half of 2016, it is down 23 per cent from the equivalent period last year.

Even so, the elements are being put in place for what could be a quite sudden and far-reaching energy transition, which could be triggered by an unexpected and sustained surge in oil prices. If China or India were to make large-scale policy commitments to electric vehicles, they would have a dramatic impact on the outlook for oil demand.

I’m also interested in Elon Musk’s Gigafactory: a lithium-ion battery factory in Nevada with a projected capacity of 50 gigawatt-hours/year of battery packs in 2018, ultimately ramping up to 150 GWh/yr. These battery packs are mainly designed for Musk’s electric car company, Tesla.

So far, Tesla is having trouble making lots of cars: its Fremont, California plant theoretically has the capacity to make 500,000 cars per year, but last year it only built 50,000. For some of the reasons, see this:

• Matthew Debord, Tesla has to overcome a major problem for its massive new Gigafactory to succeed, Singapore Business Insider, 1 August 2016.

Basically, it’s hard to make cars as efficiently as traditional auto companies have learned to do, and as long as people don’t buy many electric cars, it’s hard to get better quickly.

Still, Musk has big dreams for his Gigafactory, which I can only applaud. Here’s what it should look like when it’s done:


8 May, 2016

One of the big problems with intermittent power sources like wind and solar is the difficulty of storing energy. But if we ever get a lot of electric vehicles, we’ll have a lot of batteries—and at any time, most of these vehicles are parked. So, they can be connected to the power grid.

This leads to the concept of vehicle-to-grid or V2G. In a V2G system, electric vehicles can connect to the grid, with electricity flowing from the grid to the vehicle or back. Cars can help solve the energy storage problem.

Here’s something I read about vehicle-to-grid systems in Sierra magazine:

At the University of Delaware, dozens of electric vehicles sit in a uniform row. They’re part of an experiment involving BMW, power-generating company NRG, and PJM—a regional organization that moves electricity around 13 states and the District of Columbia—that’s examining how electric vehicles can give energy back to the electricity grid.

It works like this: When the cars are idle (our vehicles typically sit 95 percent of the time), they’re plugged in and able to deliver the electricity in their batteries back to the grid. When energy demand is high, they return electricity to the grid; when demand is low, they absorb electricity. One car doesn’t offer much, but 30 of them is another story—worth about 300 kilowatts of power. Utilities will pay for this service, called “load leveling,” because it means that they don’t have to turn on backup power plants, which are usually coal or natural gas burners. And the EV owners get regular checks—approximately $2.50 a day, or about $900 a year.

It’s working well, according to Willett Kempton, a longtime V2G guru and University of Delaware professor who heads the school’s Center for Carbon-Free Power Integration: “In three years hooked up to the grid, the revenue was better than we thought. The project, which is ongoing, shows that V2G is viable. We can earn money from cars that are driven regularly.”

V2G still has some technical hurdles to overcome, but carmakers—and utilities, too—want it to happen. In a 2014 report, Edison Electric Institute, the power industry’s main trade group, called on utilities to promote EVs [electric vehicles], describing EV adoption as a “quadruple win” that would sustain electricity demand, improve customer relations, support environmental goals, and reduce utilities’ operating costs.

Utilities appear to be listening. In Virginia and North Carolina, Dominion Resources is running a pilot project to identify ways to encourage EV drivers to only charge during off-peak demand. In California, San Diego Gas & Electric will be spending $45 million on a vehicle-to-grid integration system. At least 25 utilities in 14 states are offering customers some kind of EV incentive. And it’s not just utilities—the Department of Defense is conducting V2G pilot programs at four military bases.

Paula DuPont-Kidd, a spokesperson for PJM, says V2G is especially useful for what’s called “frequency regulation service”—keeping electricity transmissions at a steady 60 cycles per second. “V2G has proven its ability to be a resource to the grid when power is aggregated,” she says. “We know it’s possible. It just hasn’t happened yet.”

I wonder how much, exactly, this system would help.

My quote comes from here:

• Jim Motavalli, Siri, will connected vehicles be greener?, Sierra, May–June 2016.

Motavalli also discusses vehicle-to-vehicle connectivity and vehicle-to-building systems. The latter could let your vehicle power your house during a blackout—which seems of limited use to me, but maybe I don’t get the point.

In general, it seems good to have everything I own have the ability to talk to all the rest. There will be security concerns. But as we move toward ‘ecotechnology’, our gadgets should become less obtrusive, less hungry for raw power, more communicative, and more intelligent.

The Case for Optimism on Climate Change

7 March, 2016


The video here is quite gripping: you should watch it!

Despite the title, Gore starts with a long and terrifying account of what climate change is doing. So what’s his case for optimism? A lot of it concerns solar power, though he also mentions nuclear power:

So the answer to the first question, “Must we change?” is yes, we have to change. Second question, “Can we change?” This is the exciting news! The best projections in the world 16 years ago were that by 2010, the world would be able to install 30 gigawatts of wind capacity. We beat that mark by 14 and a half times over. We see an exponential curve for wind installations now. We see the cost coming down dramatically. Some countries—take Germany, an industrial powerhouse with a climate not that different from Vancouver’s, by the way—one day last December, got 81 percent of all its energy from renewable resources, mainly solar and wind. A lot of countries are getting more than half on an average basis.

More good news: energy storage, from batteries particularly, is now beginning to take off because the cost has been coming down very dramatically to solve the intermittency problem. With solar, the news is even more exciting! The best projections 14 years ago were that we would install one gigawatt per year by 2010. When 2010 came around, we beat that mark by 17 times over. Last year, we beat it by 58 times over. This year, we’re on track to beat it 68 times over.

We’re going to win this. We are going to prevail. The exponential curve on solar is even steeper and more dramatic. When I came to this stage 10 years ago, this is where it was. We have seen a revolutionary breakthrough in the emergence of these exponential curves.

And the cost has come down 10 percent per year for 30 years. And it’s continuing to come down.

Now, the business community has certainly noticed this, because it’s crossing the grid parity point. Cheaper solar penetration rates are beginning to rise. Grid parity is understood as that line, that threshold, below which renewable electricity is cheaper than electricity from burning fossil fuels. That threshold is a little bit like the difference between 32 degrees Fahrenheit and 33 degrees Fahrenheit, or zero and one Celsius. It’s a difference of more than one degree, it’s the difference between ice and water. And it’s the difference between markets that are frozen up, and liquid flows of capital into new opportunities for investment. This is the biggest new business opportunity in the history of the world, and two-thirds of it is in the private sector. We are seeing an explosion of new investment. Starting in 2010, investments globally in renewable electricity generation surpassed fossils. The gap has been growing ever since. The projections for the future are even more dramatic, even though fossil energy is now still subsidized at a rate 40 times larger than renewables. And by the way, if you add the projections for nuclear on here, particularly if you assume that the work many are doing to try to break through to safer and more acceptable, more affordable forms of nuclear, this could change even more dramatically.

So is there any precedent for such a rapid adoption of a new technology? Well, there are many, but let’s look at cell phones. In 1980, AT&T, then Ma Bell, commissioned McKinsey to do a global market survey of those clunky new mobile phones that appeared then. “How many can we sell by the year 2000?” they asked. McKinsey came back and said, “900,000.” And sure enough, when the year 2000 arrived, they did sell 900,000—in the first three days. And for the balance of the year, they sold 120 times more. And now there are more cell connections than there are people in the world.

So, why were they not only wrong, but way wrong? I’ve asked that question myself, “Why?”

And I think the answer is in three parts. First, the cost came down much faster than anybody expected, even as the quality went up. And low-income countries, places that did not have a landline grid—they leap-frogged to the new technology. The big expansion has been in the developing counties. So what about the electricity grids in the developing world? Well, not so hot. And in many areas, they don’t exist. There are more people without any electricity at all in India than the entire population of the United States of America. So now we’re getting this: solar panels on grass huts and new business models that make it affordable. Muhammad Yunus financed this one in Bangladesh with micro-credit. This is a village market. Bangladesh is now the fastest-deploying country in the world: two systems per minute on average, night and day. And we have all we need: enough energy from the Sun comes to the Earth every hour to supply the full world’s energy needs for an entire year. It’s actually a little bit less than an hour. So the answer to the second question, “Can we change?” is clearly “Yes.” And it’s an ever-firmer “yes.”

Some people are much less sanguine about solar power, and they would point out all the things that Gore doesn’t mention here. For example, while Gore claims that “one day last December” Germany “got 81 percent of all its energy from renewable resources, mainly solar and wind”, the picture in general is not so good:

This is from 2014, the most recent I could easily find. At least back then, renewables were only slightly ahead of ‘brown coal’, or lignite—the dirtiest kind of coal. Furthermore, among renewables, burning ‘biomass’ produced about as much power as wind—and more than solar. And what’s ‘biomass’, exactly? A lot of it is wood pellets! Some is even imported:

• John Baez, The EU’s biggest renewable eneergy source, 18 September 2013.

So, for every piece of good news one can find a piece of bad news. But the drop in price of solar power is impressive, and photovoltaic solar power is starting to hit ‘grid parity’: the point at which it’s as cheap as the usual cost of electricity off the grid:

According to this map based on reports put out by Deutsche Bank (here and here), the green countries reached grid parity before 2014. The blue countries reached it after 2014. The olive countries have reached it only for peak grid prices. The orange regions are US states that were ‘poised to reach grid parity’ in 2015.

But of course there are other issues: the intermittency of solar power, the difficulties of storing energy, etc. How optimistic should we be?

Ken Caldeira on What To Do

25 January, 2016

Famous climate scientist Ken Caldeira has a new article out:

• Ken Caldeira, Stop Emissions!, Technology Review, January/February 2016, 41–43.

Let me quote a bit:

Many years ago, I protested at the gates of a nuclear power plant. For a long time, I believed it would be easy to get energy from biomass, wind, and solar. Small is beautiful. Distributed power, not centralized.

I wish I could still believe that.

My thinking changed when I worked with Marty Hoffert of New York University on research that was first published in Nature in 1998. It was the first peer-reviewed study that examined the amount of near-zero-emission energy we would need in order to solve the climate problem. Unfortunately, our conclusions still hold. We need massive deployment of affordable and dependable near-zero-emission energy, and we need a major research and development program to develop better energy and transportation systems.

It’s true that wind and solar power have been getting much more attractive in recent years. Both have gotten significantly cheaper. Even so, neither wind nor solar is dependable enough, and batteries do not yet exist that can store enough energy at affordable prices to get a modern industrial society through those times when the wind is not blowing and the sun is not shining.

Recent analyses suggest that wind and solar power, connected by a continental-scale electric grid and using natural-gas power plants to provide backup, could reduce greenhouse-gas emissions from electricity production by about two-thirds. But generating electricity is responsible for only about one-third of total global carbon dioxide emissions, which are increasing by more than 2 percent a year. So even if we had this better electric sector tomorrow, within a decade or two emissions would be back where they are today.

We need to bring much, much more to bear on the climate problem. It can’t be solved unless it is addressed as seriously as we address national security. The politicians who go to the Paris Climate Conference are making commitments that fall far short of what would be needed to substantially reduce climate risk.

Daunting math

Four weeks ago, a hurricane-strength cyclone smashed into Yemen, in the Arabian Peninsula, for the first time in recorded history. Also this fall, a hurricane with the most powerful winds ever measured slammed into the Pacific coast of Mexico.

Unusually intense storms such as these are a predicted consequence of global warming, as are longer heat waves and droughts and many other negative weather-related events that we can expect to become more commonplace. Already, in the middle latitudes of the Northern Hemisphere, average temperatures are increasing at a rate that is equivalent to moving south about 10 meters (30 feet) each day. This rate is about 100 times faster than most climate change that we can observe in the geologic record, and it gravely threatens biodiversity in many parts of the world. We are already losing about two coral reefs each week, largely as a direct consequence of our greenhouse-gas emissions.

Recently, my colleagues and I studied what will happen in the long term if we continue pulling fossil carbon out of the ground and releasing it into the atmosphere. We found that it would take many thousands of years for the planet to recover from this insult. If we burn all available fossil-fuel resources and dump the resulting carbon dioxide waste in the sky, we can expect global average temperatures to be 9 °C (15 °F) warmer than today even 10,000 years into the future. We can expect sea levels to be about 60 meters (200 feet) higher than today. In much of the tropics, it is possible that mammals (including us) would not be able to survive outdoors in the daytime heat. Thus, it is essential to our long-term well-being that fossil-fuel carbon does not go into our atmosphere.

If we want to reduce the threat of climate change in the near future, there are actions to take now: reduce emissions of short-lived pollutants such as black carbon, cut emissions of methane from natural-gas fields and landfills, and so on. We need to slow and then reverse deforestation, adopt electric cars, and build solar, wind, and nuclear plants.

But while existing technologies can start us down the path, they can’t get us to our goal. Most analysts believe we should decarbonize electricity generation and use electricity for transportation, industry, and even home heating. (Using electricity for heating is wildly inefficient, but there may be no better solution in a carbon-constrained world.) This would require a system of electricity generation several times larger than the one we have now. Can we really use existing technology to scale up our system so dramatically while markedly reducing emissions from that sector?

Solar power is the only energy source that we know can power civilization indefinitely. Unfortunately, we do not have global-scale electricity grids that could wheel solar energy from day to night. At the scale of the regional electric grid, we do not have batteries that can balance daytime electricity generation with nighttime demand.

We should do what we know how to do. But all the while, we need to be thinking about what we don’t know how to do. We need to find better ways to generate, store, and transmit electricity. We also need better zero-carbon fuels for the parts of the economy that can’t be electrified. And most important, perhaps, we need better ways of using energy.

Energy is a means, not an end. We don’t want energy so much as we want what it makes possible: transportation, entertainment, shelter, and nutrition. Given United Nations estimates that the world will have at least 11 billion people by the end of this century (50 percent more than today), and given that we can expect developing economies to grow rapidly, demand for services that require energy is likely to increase by a factor of 10 or more over the next century. If we want to stabilize the climate, we need to reduce total emissions from today’s level by a factor of 10. Put another way, if we want to destroy neither our environment nor our economy, we need to reduce the emissions per energy service provided by a factor of 100. This requires something of an energy miracle.

The essay continues.

Near the end, he writes “despite all these reasons for despair, I’m hopeful”. He is hopeful that a collective change of heart is underway that will enable humanity to solve this problem. But he doesn’t claim to know any workable solution to the problem. In fact, he mostly list reasons why various possible solutions won’t be enough.

Underestimating Renewables

4 January, 2016

The International Energy Agency, or IEA for short, is an autonomous intergovernmental organization based in Paris. They were established in the 1970’s after the OPEC embargo sent oil prices to new highs. Their main job is to guess the future when it comes to energy production. They do this in their annual World Energy Outlook or WEO.

I’ve tended to trust their predictions, since they seem to have a lot of expertise and don’t seem to have a strong axe to grind. They believe global warming is a serious problem and they’ve outlined some plans for what to do.

However, I’m now convinced that they’ve consistently underestimated the growth of renewable energy. Not just a little—a lot.

This is bad news in a way: who can I trust now? But of course it’s mainly good news! I am now more optimistic about the potential of wind and solar power.

To explain what I mean, I’m just going to quote a chunk of this article:

• David Roberts, The International Energy Agency consistently underestimates wind and solar power. Why?, Vox, October 12, 2015.

Here goes:

David Roberts on the IEA

That the IEA has historically underestimated wind and solar is beyond dispute. The latest look at the issue comes from Energy Post editor Karel Beckman, who draws on a recent report from the Energy Watch Group (EWG), an independent Berlin-based think tank. The report analyzes the predictive success of previous WEOs.

Here’s the history of additions to electric generation capacity by renewables excluding big hydro, along with successive WEO projections:

[Chart from Energy Watch Group. Click to enlarge.]

As you can see, IEA keeps bumping up its projections, but never enough to catch up to reality. It’s only now getting close.

It gets even worse when you dig into the details. Here’s the bill of particulars:

• WEO 2010 projected 180 GW of installed solar PV capacity by 2024; that target was met in January 2015.

• Current installed PV capacity exceeds WEO 2010 projections for 2015 by threefold.

• Installed wind capacity in 2010 exceeded WEO 2002 and 2004 projections by 260 and 104 percent respectively.

• WEO 2002 projections for wind energy in 2030 were exceeded in 2010.

Other, independent analysts (like those at Bloomberg New Energy Finance and Citi) have come closer to accurately forecasting renewables. The only forecasts that match IEA’s inaccurate pessimism are those from the likes of BP, Shell, and Exxon Mobil.

Here are IEA’s wind and solar projections broken out, from a 2014 post by the folks at eco-consultancy Ecofys:

[Click to enlarge.]

Back in 2013, energy analyst Adam Whitmore took a look at the IEA’s track record on renewables. He found it abysmal, like everyone else. This year, he returned to the WEO to see if it has improved and found that, well, it hasn’t.

Here he shows the rate of growth in annual installations of renewables, and what the IEA projects for the future:

[Click to enlarge.]

(The dashed lines are the standard WEO projections, what happens if nothing changes. The dotted lines are from the “bridge scenario” in the WEO Special Report on Energy and Climate Change, which is supposed to represent some policy ambition.)

As Whitmore says, it’s possible that the rate of solar PV installations will suddenly plunge by some 40 percent and then enter a long steady-state period, but there’s no reason to think it’s particularly plausible.

For more

Roberts goes on to analyze various possible reasons for the IEA’s consistent underestimates. They’re worth reading, but none of them seems like an obvious smoking gun.

I suppose if I were very careful I would check all the graphs and numbers in Roberts’ article, but I’m inclined to trust them. He’s getting them from various sources; this is a factual issue that can be easily checked, and I haven’t seen anyone arguing the other side.

If you want to check some numbers yourself, you can download these free books:

WEO 2011.

WEO 2010.

WEO 2009.

WEO 2008.

WEO 2007.

WEO 2006.

The following report, mentioned above, goes into more detail about the IEA’s failures:

• Matthieu Metayer, Christian Breyer and Hans-Josef Fell, The projections for the future and quality in the past of the World Energy Outlook for solar PV and other renewable energy technologies, Energy Watch Group, 2015.

They write:

Summing up, the IEA keeps ignoring the exponential growth of new renewable energies such as solar and wind, and does not learn from its past mistakes.

But this leaves me with a question. Who is doing the best job of predicting energy trends? This is where we could really use a well-developed, easily accessed prediction market.