Which party would these Intentional Leaders Belong too

[OSR stands with Israel]

Suppose it's only based on Foreign Policy, Domestic, and Economic and not Social or Religious Issues

Cameron- Democratic
Bibi-   Republican
Modi-  Republican
Merkel-  Democratic
Putin- Constitution
Valls- Socialist

[Sumner 1868]

Change Cameron and Merkel to Republican and Putin to American Independent Party.

[Lief 🗽]

Cameron would absolutely not be a Democrat in the United States.

[Famous Mortimer]

Suppose it's only based on Foreign Policy, Domestic, and Economic and not Social or Religious Issues

Cameron- Democratic
Bibi-   Republican
Modi-  Republican
Merkel-  Democratic
Putin- Constitution
Valls- Socialist

A worthy topic for a thread but good God, you know nothing  about foreign politics. Valls would be a member of the SPUSA? That's crazy. He barely fits in with the PS and the SPUSA is about a thousand times more left-wing than the PS.

Cameron - Republican, and he would feel free to be much more right-wing if he lived in the US
Bibi - Republican
Modi - Republican
Merkel - Probably a Democrat, it isn't out of the question that she would identify with the Republicans but she would probably get forced to switch at some point
Putin - Republican. He's socially conservative and he's shown a slight preference for the right over the left (preferring United Russia to Fair Russia). Mostly though he is concerned with being in power. For that reason, he would never join a fringe group like the Constitution Party if he were an American politician
Valls - Democrat, a horrible DLC Democrat. He would be obsessed with the deficit though and no Democratic voters would like him

[Middle-aged Europe]

Change Cameron and Merkel to Republican and Putin to American Independent Party.

Merkel is probably to left of Hillary politically... so please explain why Hillary isn't a Republican then.

[🦀🎂🦀🎂]

Merkel is a weathervane, who runs with public opinion.

[Murica!]

Cameron- Republican
Bibi-    Republican
Modi-  Republican
Merkel-  Democratic(she's definitely to the left of Hilary)
Putin- Republican economic populist
Valls- Democratic

[Celebi]

Cameron- Democrat (Nobody could become prime minister in any European country if their policies would be anywhere close to Republicans)
Bibi-   Joe Lieberman style Democrat
Modi-  Republican
Merkel-  Progressive Democrat, probably even to the left of Bernie Sanders
Putin- probably Southern Democrat (socially conservative, economically slightly liberal)
Valls- Socialist (similar to Bernie Sanders but more left-wing)

[🦀🎂🦀🎂]

Let's not confuse politicians' policies (I.e. Stances on "issues") with their ideologies.

[VPH]

Cameron-centrist independent, probably leans Democratic
Bibi-Independent who usually votes Republican but occasionally Democratic
Modi-Republican
Merkel-Democratic
Putin-Republican (Tea Party for sure)
Valls-Democratic or Green

[Middle-aged Europe]

Putin-Republican (Tea Party for sure)

I don't really see Putin as a true Tea Party believer (or even Constitution Party member), since he's probably too smart for that kind of thing. He may pretend to be smypathizing with the Tea Party, but that would just be a means to an end to advance his own political ambitions.

A hardline neocon in the mold of Cheney or Rumsfeld would have been a better analogue to Putin. Except that neocons have become a dying breed in America. So maybe he's an ex-neocon who's pandering to the Tea Party for strictly opportunistic reasons.

[H. Ross Peron]

Harper-Republican (probably pretty conservative but not Tea Party)
Cameron-Republican (probably would have views akin to Charlie Baker or possibly Mark Kirk)
Hollande-Democratic
Merkel-Democratic (would basically be a Dianne Feinstein clone)
Modi-Republican
Putin-One of the Russophile paleocon Republicans, possibly like Pat Buchanan
Valls-DLC Democrat
Abe-Democratic (again of the Dianne Feinstein variety)

[SATW]

Cameron - Moderate Republican (I like the Charlie Baker comparison)
Harper - Conservative Republican (George W. Bush)
Hollande - Liberal Democrat (Not really sure on who he'd be in American politics though...)
Netanyahu - Conservative Republican (Mitt Romney + Rudy Giuliani  + John Boehner mix)
Merkel - Moderately Liberal Democrat (Hillary Clinton fits)
Modi - Moderately Conservative Republican (Not sure who matches in American politics)
Putin - Conservative Republican (Jim DeMint + John Boehner mix)
Valls - DLC/Third Day Democrat (Joe Lieberman?)

[🦀🎂🦀🎂]

The other peculiar thing about BiBi is that aside from his (in)famous reputation, he is considered a moderate in Likud and the Israeli right-wing in general.

[SATW]

The other peculiar thing about BiBi is that aside from his (in)famous reputation, he is considered a moderate in Likud and the Israeli right-wing in general.

Yup. He likes to sit in the middle, ideologically speaking, of his coalitions. Of course, moderate here is a very ill-defined term. In Israel, being "moderate" means your views aren't as emotion fueled. I don't think there is much that separates Bibi and people like Danny Danon on foreign policy besides rhetoric.

In terms of religiosity, he is definitely one of the more moderate Likudniks (He's essentially Israel's Newt Gingrich, marriage wise.

[Linus Van Pelt]

This is a really strange question and I am surprised so many posters think they understand what is being asked.

I mean, if we're supposed to hold fixed their publicly stated policies and ignore the psychological or historical factors behind those policies, then I do understand what is being asked. But then the answer should be: all the leaders of rich democracies would be Democrats, albeit hawkish ones in some cases. Even the Likud supports universal health care and legal abortion. But that doesn't seem to be how people are interpreting it, and indeed is depicted as a sort of naive way to answer the question; instead the question is about the actual humans. But what counterfactual scenario is described by "if David Cameron were American"? When does he move to America? At age 2? At age 21? Tomorrow? Would not this counterfactual biography likely lead to his values changing in an unpredictable way?

[Hydera]

David Cameron - Moderate Establishment Republican, Closer to the right-of-center. Due to the threat of UKIP eating into his base its his backbenchers thats making him take a tougher stance on the EU and Immigration when he didn't care much for those issues before.

Bibi - Tea party-ish Republican. Very nationalist.

Modi - Formerly nationalist Hindutva, who made some statements about islam back when he was the head of gujarat. and moderated a lot over time to appeal to the whole of the Indian electorate. Reluctant establishment Republican whose that way.

Putin - Constitution party, American independent, Ultra-tea party Republican? Formely less focused on social issues when he became President and over time since the mid-2000's adopted a lot of socially conservative stances. And Always been a strict hardline Nationalist.

Merkel - Establishment / Mainstream republican without a backbone. She supported Green energy and shutting down Nuclear when it became popular and very disadvantageous for her if she didn't, due to the backlash in german society since Fukushima.

Valls - DLC-er/Liberal Republican. Socially Liberal and fiscally conservative.

Harper - Establishment Republican. Doesn't care much about social issues. But right-wing on economics.

Hollande - (Phase 1[2012-2013]) Establishment Democrat. (Phase 2[2014+) DLC-er Democrat/Moderate democrat whose only leftwing on social issues and dropped the leftwing on economics.

Bonus:

Abbott - Conservative Republican. Strongman on stopping asylum seeker boats, Fiscally and socially conservative.

Renzi - Left of centre Democrat

John Key - Libertarian/Socially Liberal Republican

I think i'm finding a pattern here. Most heads of right-wing parties are very moderate compared to the political landscape in the US. Also the heads of left-wing parties are also very moderate and sometimes do not differ much with their right-wing counterparts.