> In the US there have been other parties that have put presidents in office

There have never been more than two nationally-competitive parties in the US. There have been times when a party collapsed and subsequently was replaced (the Federalists by the Whigs, and the Whigs by the Republicans.)

> Theodore Wilson was a Progressive Party candidate

Presumably, you mean (former) President Theodore Roosevelt, who, formed the Progressive Party in a factional split from the Republican Party over his dissatisfaction with his hand-picked successor.

And who didn't win, so isn't an illustration of your claim that parties other than the two major ones have put Presidents in office.

> and in the UK, which also has a first-past-the-post system, there are multiple parties and the country is currently governed by a coalition of Conservatives and Liberal Democrats

The UK and US differ in that, in additional to FPTP voting for members of the national legislature, the US has a separately (and indirectly) elected strong executive using a means that is even more strongly favors the two major parties than simple single-member district FPTP elections do; this not only gives a greater tendency for a major party to win control of the administration by winning the Presidential election, it further limits the expected influence of non-major party candidates for the national legislature, which further reduces their prospects.

So, yes, there is a well-understood structural reason in the electoral that the US has even less representative government and a stronger tendency to a two-party system (even though it has weaker parties) than the UK, even though both use FPTP for the national legislature.

Theodore Roosevelt indeed - I jammed his name together with Woodrow Wilson, his Democratic opponent. Wilson beat him handily, but Roosevelt still outpolled the GOP candidate, WH Taft.

You are quite right about the key difference with the US having an elected executive vs the parliamentary democacy system of the UK, but I don't see how FPTP prevent the election of Congressional candidates from outside the two major parties. There are usually a few independents in either chamber of Congress, but I don't see any particular reason why another party couldn't make a showing if it were willing to put in the organizational leg-work.

In my (limited) experience American politicians and parties are excessively focused on elective office; being from Ireland myself I think long-term success stems from building a solid local constituency. So for example, I think it's a complete waste of time for the Green party to run candidates in the US presidential election, instead of working to capture a few seats in Congress or in state legislatures. I have been involved in a few such local campaigns, and what I've observed is that on failing to win a major election the candidates tend to exit politics instead.

> I don't see how FPTP prevent the election of Congressional candidates from outside the two major parties.

It doesn't prevent it, it just makes it extremely rare. The reason is, essentially, Tragedy of the Commons: for each individual voter, the most strongest result from voting for a minor party candidate rather than the least-opposed major party candidate is to make it more likely that their most-opposed major party candidate will win over their least-opposed major party candidate.

> There are usually a few independents in either chamber of Congress

Since WWII, there's sometimes a few independents in Congress in total, but rarely more than 1-2 in either chamber, and often none in one or both chambers. Things were a little different earlier (in part because the two-party system in each state was sometimes not the same as the national two-party system; e.g., in Minnesota for a considerable period, the two competitive parties were the Farmer-Labor Party and the Republican Party.)

And even the very small number of independents in Congress overstates the non-party influence; very often the "independents" in Congress are either people who were elected as members of one party and then defected after being elected (sometimes being re-elected as independents once they have secured the advantages of incumbency), and at other times they are independents that one of the two major parties has chosen not to oppose in general elections. (Note that the two independents currently in the US Congress, both in the Senate, include one of each of those descriptions.)

I appreciate that - I'm familiar with Condorcet's and Arrow's theorems. I'm not a fan of FPTP myself (as I come from a country with proportional representation, and quite like that it's how local elections are run where I live); I just don't think it's deliberately engineered to effectively prevent the formation of other parties, although I certainly agree that it's frequently gamed to that end.

FPTP itself is not deliberately engineered to lead to two parties and I doubt that was the intent of the framers anyways. For a time at the beginning of U.S. government the whole notion of strong political parties was considered bad for governance anyways; people were supposed to represent their constituents or their state.

However nowadays the two major parties certainly do cooperate in ensuring that there remain only two major parties, rather aggressively going even further than FPTP would otherwise lead to in keeping additional political parties weak. It's easier to get elected without a party affiliation at all than to be elected as a party other than D or R.

> I just don't think it's deliberately engineered to effectively prevent the formation of other parties

Whether it is "deliberately engineered" to do that or not, it has a fairly well-demonstrated effect of doing that compared to systems which provide more proportional results. Intent is pretty much irrelevant.

One of the biggest reasons third parties don't make it is financing. If you have a lot of cash that you want to give to a party, you give to a party that will likely be elected and might return the favor. If you have A LOT, you give to both parties. What wealthy contributors are going to give their money to a third party when they can afford to back two horses?

Also, gerrymandering. It's a major, major factor in maintaining the status quo. The UK has picked up on this trend (well, they've done it before, but it's kicked up a notch), and the conservatives been quietly moving parliamentary boundaries for the last few years.