Michael Huemer’s article ‘Is There a Right to Immigrate?’ tries to show that restricting immigration violates the prima facie right to be free from harmful coercion, a right which is not overridden by the points usually raised in defence of restriction. The approach of using a thought experiment based on certain widespread intuitions (rather than taking a philosophical theory or ideological orientation to be true and deriving policies from it) is very sensible, and makes the whole article more relevant and persuasive.
I think the article succeeds as an argument for economic immigration, and ideally it may justify an open-borders policy for the US. The problem is in the claim that its arguments "apply equally well to other countries." On the contrary, most of its responses to objections to unlimited immigration become naive when applied to other developed countries, such as Britain and elsewhere in western Europe. A related problem is that the article ostensibly aims to defend immigration as such, yet its central thought experiment refers strictly to two parties who want to trade with each other (starving Marvin and an unspecified shop owner) but are prevented from doing so by a third party. What hasn't been addressed is the large number of people who would come purely to receive certain benefits offered in the developed world. For example, many of those countries have socialised health care, whose legitimacy depends on the ability and willingness to treat everyone, rich or poor, without charging them. A flood of critically ill immigrants would destroy that institution (or more likely, the government under which open borders were introduced would be voted out, and restrictions would be reintroduced).
The argument for preventing that kind of immigration is not the same as the argument that, "because of a policy one has voluntarily adopted, if one did not coerce one’s victim in this way, one would instead confer a benefit on the person that one does not wish to confer." It is not the same because it does not infringe the freedom of association to stop people from entering a country purely in order, say, to gather outside its hospitals, creating an imperative to treat them (by that institution's ethical/social standards) and thereby destroying an institution set up to provide (relatively) high quality health care to anyone who needs it.
(If one has some absolutist conception of rights, one might say it impinges on the prospective immigrants' freedom of movement. But the argument in the article is set up around not assuming any such view, so that doesn't matter.)
This sort of concern is not confined to the existence of government welfare; that is just a factor which would attract non-economic immigrants. The general problem is this. In a country like Britain – which I will use as a counterexample from here on – institutions work only in virtue of shared knowledge of their members. It is a special kind of society, in which people have learnt to deal with each other and manage conflicts without violence. Because Britain does not currently have sufficient mechanisms (be they policies or informal traditions) for getting immigrants to assimilate, unrestricted immigration would threaten the existence of social norms which allow this kind of society to exist. For example: today in Britain, it is outside the realm of ordinary experience to come home and find someone ransacking the house, who, when confronted, pleas that he needs money to save his child’s life. That is the case partly because society is arranged in such a way that no one ever gets into such a desperate situation (an arrangement which would no longer work if swamped). But it is also because the vast majority of people respect the law, and would find legal, peaceful ways to manage desperate situations. Law enforcement in Britain relies on that fact. It could not cope with vast numbers of people who were not law-abiding in the British sense, and many of whom preferred prison to their tyrannical or war-torn countries of origin.
Huemer dismisses the 'cultural change' objection with a thought experiment about a country becoming Buddhist from the inside. But the objection has force when it is acknowledged that change might be imposed on a society from the outside, and that it involves a threat of violence, in the sense that members of the foreign culture do not recognise the non-violent institutions which make the society of their new place of residence what it is. Again, this is not an issue for Huemer's example country, partly because the US is so large (it would take a far greater number of immigrants to have any of the above effects), and, more importantly, because it has an ethos which strongly encourages immigrants to 'become American'. The same has become far less true of Britain over the last few decades, where that sort of attitude would nowadays be considered churlish.
Huemer addresses the fear of general societal collapse in section 3.5, where he disputes that any such thing would happen, apparently because foreigners, no matter where they come from or what their circumstances, would rather be with their families and stay in their own country (to which they are proud to belong) than move to a richer one. This is just factually false. To point out that Americans rarely move between states is to make a false comparison. Every American state has a tolerable standard of living. People are not dying of hunger in America. So of course their incentive to move is comparatively weak. The central example of the paper is based on the fact that many people who want to immigrate will otherwise die. That – and also much lesser plight than that – overrides any preference to stay with family or to stay in one's hometown.
This is especially true of an area of concern already raised: immigrants who come expressly to receive health care. They will die if they do not come. So the author's dismissal of the claim that a country with open borders would be overloaded with immigrants (on the basis that they would rather stay with their families) is too hasty.
It is strange that Huemer attaches significance to the fact that only 13 million people have made some effort toward moving to the US, and then admits that many others presumably make no effort, being aware of the draconian restrictions – not acknowledging that the vast majority of people who would rather live in the US are preemptively put off from making any such effort, which renders the 13 million figure meaningless. He does concede that the 'immigrant flood' worry means it might be better to open borders gradually, adding an extra million to the cap each year. Again, this may work for the US. It would not work for most developed countries.