What type of government system has the following characteristics? i. a monarch is the head of state. ii. the powers of the monarch are limited by a constitution. iii. citizen vote for members of a legislative body. iv. the legislative body chooses the head of government.

Any of the following could apply to the scenario detailed in your question:

However the most appropriate would be Constitutional Republic.

Explanation:

Federation - a group of states with a central government but independence in internal affairs

Liberal Democracy - representative form of government that does not stick too closely by traditional values, rather ideas of liberalism or new opinions.

Presidential System - a government where there is a head of a so called "executive branch" and is separate from other governing bodies in the nation such as the legislative or judicial body.

Federal Republic - a republic in which states are granted certain governing powers that cannot be revoked by a higher or national governing body.

Constitutional Republic - a government where all political leaders are elected by the public in some way (whether indirect or direct) and all rules are written in a constitution.