In the United States and most other countries in the British political tradition, you cast your vote for an individual and a party designation is just a helpful hint.
And, of course, I know of no political system anywhere in which there is actually a legal obligation for elected officials to keep the promises that they make on the campaign trail - if there was, our jails would be absolutely packed with politicians.
In general, in these systems, you can change your political party without a new election. Indeed, there are notable examples of individuals doing so. For example, U.S. Senator Ben Nighthorse Campbell from Colorado was elected as a Democrat in the November 1992 election and changed his party affiliation to Republican in March 1995.
But, really, a legislative political party designation is primarily a designation that describes how one is likely to vote on issues. Any legislature in which elected officials get to decide how they cast their own votes, necessarily must allow for the possibility that some group of elected legislators with a particular political party designation cast their voters differently than other elected legislators with the political party designation.
Whether or not they formally disaffiliate from the political party that they were elected as members of or not, a group of elected legislators who start to vote as a group differently from other members of their own party or parties is inevitably going to acquire an informal name for their faction (e.g. "Blue Dog Democrats", "Dixiecrats", "Tea Party Republicans", R.I.N.O.s i.e. Republicans In Name Only, Rockefeller Republicans, etc.).
Also, while a new election isn't held when an elected legislator either resigns from a party or is ejected from one, that doesn't mean that tools of party discipline don't exist. In recent instances in the U.S. Congress and in the Colorado General Assembly where legislators have switched parties midterms, those legislators have been stripped of committee seats allocated to them by their political party and otherwise denied privileges that they previously held as party members in good standing. In a parliamentary system, a party switcher could have his or her ministry in cabinet taken way by the leadership.
But, allowing for party switching is valuable for the long term health of the political party system in a democracy. Both in the U.S. and abroad, one of the most common ways for new, viable political parties to come into being is for existing elected officials to change party affiliation to the new political party.
For example, Abraham Lincoln and many of the other founding members of the Republican Party, were formerly members of the Whig Party. Similarly, in the DIM.AR (Democratic Left) political party in Greece was formed mostly by deputies who had seceded from the SY.RIZ.A. political party, in anticipation of the May 6, 2012 election there.