Let's compromise. I promise to be totally clear, transparent, and straightforward in my ticket purchases as long as the airlines are totally clear, transparent, and straightforward in their ticket pricing.
And you will make available all the information that goes into that process, the algorithms applied to that information, and the prices offered to other people?
Air travel is not a free market - the capital requirements are insane, the cost of fuel is often subsidized by the government (you cannot tax or excise it IIRC), you have a lot of regulations and so on ...
Air travel in the US is highly regulated, but the market is actually very free. If you have sufficient capital you can absolutely start a new airline and be carrying paying passengers in under a year. In fact you could probably do it in a few months by leasing existing aircraft and contracting with existing aviation service companies for most operations. The FAA actively supports new ventures and will work with them on the approval process.
Regulation is part of a free market, but governmental regulation is not (i.e., regulation imposed by a monopolistic entity).
There are many forms of private governance and regulation that protect consumers. That's not to say free markets are utopias, but believing that governments are the only source of regulation is incorrect. In fact, in many cases private governance is far more effective (e.g., the private regulation Uber is subject to is stronger and more efficient than the governmental regulation traditional taxis are subject to).
See "Private Governance" by Edward Stringham for some good examples of market governance in action. The book received the following review from Peter Thiel:
"Stringham dispels state-worshipping fiction with historical fact to show how good governance has preceded Leviathan, ignores it when necessary, and can surpass it when it fails."
> Regulation is part of a free market, but governmental regulation is not
Until someone comes, holds a gun to your face and takes your sandwich. Then you'll be thankful for government regulation.
I'm absolutely certain that the government's (attempt of a) monopoly on violence is one of the most crucial aspects of free markets. Another is contract law.
Are you sure? I've never heard another free market capitalist argue that government regulations are an important part of how their ideal market works. Can you point out any free market economists that have argued for government regulation?
That's because those free market capitalists are (at best) hypocrites or (at worst) stupid. Obviously capitalism relies on regulation - of property rights, IP rights, contract laws, bans on fraud and insider trading (although opinions are mixed on that last one), ...
Regulations that make possible entrance to a market - standards, forced ineroperability, common carrier, dumb pipes etc - are generally good and provide more efficient market.
Regulations that prevent entrance to a market - by artificially rising the capital requirements to the impossible, are probably not helping the free market.