Nonetheless, let's push this metaphor further, proceeding as if some sort of vote is taking place, even if one that falls far short of "free and fair" voting standards. There are many conventional ways to determine who "wins" the vote, such as looking at percentage of foreign-born population in various countries, which says something about popular immigration destinations. But there are also many more formal voting systems if we really take this literally.
Emigration as ranked voting
Here I'm going to tabulate the results of the "vote" patterned on the one-country-one-vote model of the UN General Assembly. That tends to produce results that roughly track broad global consensus across many countries, but not population-weighted consensus, since Denmark (population 5.5 million), China (population 1.3 billion), and Tuvalu (population 10.5 thousand) each receive one vote. For immigration, this has the benefit of telling us something about how broadly popular a country is as a destination from many source regions.
Instead of UN members, the members of the voting population will be the 231 jurisdictions recognized for migration-statistics purposes by the World Bank, which publishes data on bilateral migration flows. These jurisdictions do include the UN members, and additionally include unrecognized countries (e.g. Taiwan), legally separate jurisdictions for migration purposes (e.g. Hong Kong), and de-facto separate jurisdictions for migration purposes (e.g. the Palestinian Territories).
Each jurisdiction casts its ballot by ranking how popular each possible emigration destination is from the perspective of its emigrating population. Consider emgirants from the USA. The largest number of American emigrants, as of 2000, headed to Mexico, with Canada the second-biggest destination. We can treat this as a ranked-voting ballot, with the USA marking down Mexico as #1 on its ballot, Canada as #2, and the rest likewise ranked in descending order of American-emigrant count.
Once every jurisdiction casts a ranked ballot, we can compute an overall ranking out of those votes. The details of ranked-voting resolution are a bit involved, but the basic idea of the Condorcet method is that we look at pairwise matchups. For how many countries is Canada a more popular emigration destination than France, and for how many the reverse? The winner should be the country that wins all such pairwise matchups (if any), with some complexity to deal with edge cases.
Results
The World Bank currently provides data at five snapshots in time: 1960, 1970, 1980, 1990, and 2000. Here are the top 20 vote-winners for each, with thanks to the Condorcet Internet Voting Service for the actual tallying. Note that all jurisdictions use current names and definitions, even in previous periods.
| Rank | 1960 | 1970 | 1980 | 1990 | 2000 |
|---|---|---|---|---|---|
| 1 |  USA |
USA |
USA |
USA |
USA |
| 2 |  France |
 Canada |
Canada |
Canada |
Canada |
| 3 | Canada |
France |
 UK |
 Germany |
Germany |
| 4 | UK |
UK |
 Australia |
Australia |
France |
| 5 | Germany |
Australia |
Germany |
UK |
Australia |
| 6 | Australia |
 Italy |
France |
Italy |
UK |
| 7 | Italy |
Germany |
Italy |
 India |
 Netherlands |
| 8 |  Switzerland |
 South Africa |
 Sweden |
France |
Italy |
| 9 |  Brazil |
 DR Congo |
Switzerland |
 Spain |
Spain |
| 10 | South Africa |
India |
 Nigeria |
Switzerland |
Sweden |
| 11 | India |
 Hungary |
 New Zealand |
Sweden |
Switzerland |
| 12 |  Argentina |
 Belgium |
South Africa |
 Greece |
 Denmark |
| 13 |  Austria |
Switzerland |
Belgium |
Brazil |
 Norway |
| 14 | Belgium |
Austria |
Denmark |
Denmark |
New Zealand |
| 15 | Denmark |
Sweden |
DR Congo |
Austria |
Austria |
| 16 | Hungary |
Argentina |
Austria |
New Zealand |
Greece (tie) |
| 17 | New Zealand |
New Zealand |
Hungary |
Norway |
 Ireland (tie) |
| 18 |  Mexico |
Mexico |
Norway |
Belgium |
 Israel |
| 19 |  Zimbabwe |
Nigeria |
 Egypt |
Hungary |
Belgium (tie) |
| 20 |  Sudan |
 Pakistan |
 Zambia |
Argentina |
South Africa (tie) |