In first past the post bloc voting, each voter places n Xs on the ballot paper, where n is the number of candidates to be elected. The n candidates with the highest number of votes are elected.
The bloc voting system is potentially unrepresentative of minorities, by allowing complete landslide majorities for the group of candidates with the highest level of support, though it does tend to lead to greater agreement among those elected. Like first past the post methods, small cohesive groups of voters can overpower larger numbers of disorganised voters who do not engage in tactical voting. One potential remedy for this effect is cummulative voting allowing voters to cast more than one vote for their favoured candidate.
Bloc voting has its origins in common law [can someone confirm or deny this?]. It was used in the Australian Senate from 1901 to 1948 and is often used to elect the boards of directors of corporations.
Partial block voting involves each voter receiving fewer votes than the number of candidates to be elected. This can enable reasonably sized minorities to achieve some representation. It is used in Gibraltar, where each voter has 8 votes, and 15 seats are open for election: the usual result is that the most popular party wins 8 seats and forms the administration, while the second most popular wins 7 seats and forms the opposition. If each voter only receives one vote then partial bloc voting reduces to a single non-transferable vote.
In preferential bloc voting, each voter places the numbers 1..n on the ballot paper. Candidates with the smallest tally of first preference votes are eliminated (and their votes transferred) until a candidate has more than half the vote. The system is re-started n times with the elected candidates removed and all votes returning to full value.
Block voting also describes a system of winner takes all decision-taking whereby the vote of an entire electoral unit is cast in line with the majority decision of that unit (i.e. discounting any contrary votes). This is the system used by most States for the U.S. Electoral College. It is also used in the UK by the Trades Union Congress; in a irony of history, it was introduced in 1895 by supporters of the Liberal Party to prevent or delay the establishment of the Labour Party, and it took the Labour Party from 1900 until 1993 to remove it from its own structures.