Instead of an Elected President which has now become very messy, we should consider the Australian system of a Senate that has significant powers to review major decisions taken by the government.
Here is a description of how the Australian Senate works.
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The Australian Senate is the upper house of the bicameral Parliament of Australia, the lower house being the House of Representatives. The composition and powers of the Senate are established in Chapter I, Part II of the Australian Constitution. There are a total of 76 senators: 12 senators are elected from each of the six states (regardless of population) and two from each of the two autonomous internal territories (the Australian Capital Territory and the Northern Territory). Senators are popularly elected under the single transferable vote system of proportional representation.
Unlike upper houses in most Westminster parliamentary systems, the Senate is vested with significant power, including the capacity to block all legislation, including Budget and Appropriation Bills, initiated by the government in the House of Representatives, making it a distinctive hybrid of British Westminster bicameralism and US-style bicameralism. As a result of proportional representation, the chamber features a multitude of parties vying for power. The governing party or coalition, which has to maintain the confidence of the lower house, has not held a majority in the Senate since 2005-2008 (and before that since 1981) and usually needs to negotiate with other parties and Independents to get legislation passed.[4]
Senators normally serve fixed six-year terms (from 1 July to 30 June), unless the Senate is dissolved earlier in a double dissolution. Following a double dissolution half the state senators serve terms ending on the third 30 June following the election (i.e. slightly less than three years) with the rest serving three years longer. The term of the territory senators expires at the same time as there is an election for the House of Representatives. There is no constitutional requirement for the election of senators to take place at the same time as those for members of the House of Representatives, though the government usually synchronises election dates.
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