What is the political platform of the Republicans?

Remove government influence in economy, increase government capacity to police the US and the world, promote traditional christian values.

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There is no one single platform for the Republicans just like there is not one single one for the Democrats.

Progressive Republicans, sometimes referred to as RINOs tend to side with Democrats on many issues ranging from abortion to taxes to foreign policy. Examples include Olympia Snow, Susan Collins and some extent John McCain

Neo-Conservatives is a school of thought based on a number of Democrat "defections" in the 1970's. NeoCons maintain their belief in domestic social programs and big government while also supporting a hawkish foreign policy. Neocons came to power in 2000 with the election of George W Bush.

Traditional Conservative Republicans, referred to as Paleo-Cons by the Neocons believe in limited government and limited foreign involvement. Very close to libertarians.

You also have single-issue Republicans who vote Republican on issues ranging from abortion, gay marriage, taxes, support for a foreign nation (like Israel or Taiwan) etc.