Elections cannot simply select a single ruler who represents all voices. In the best case, an election selects a Condorcet candidate—a single representative of the overall will of the people, but not the individual will.
This fact lead to the creation of parliamentary chambers to control the power of executives. A City may have a Council and a Mayor, where the Council determines or legislates what powers the Mayor has, and represents groups of voters. This represents the City only geographically and not ideologically.
On larger scales, a governed body breaks down into geographical districts with representation in a House and a Senate. Houses tend to have more representatives, and the United States House of Representatives represents smaller geographical districts within the States represented as a whole by Senators.
This structure still fails to represent ideologically. A small amendment to this political theory will dramatically increase representation.
The Proportional House
For a geographical area represented by a single at-large power, its House chamber must represent proportionally. The House must elect at least three per geographical district represented in the House, and must do so by a voting method such as Single Transferable Vote.
As seen above, the House represents proportionally, while a Senator represents an overall population. The Senator may represent the same districts as the House, as with a State’s legislative districts each receiving one Senator and three Delegates; or it may represent several districts, as with the United States Senate elected by populations of entire States, each with a number of geographical districts electing their own representation in the United States House of Representatives.
Houses as such will tend to include the competing views of subsets of the population. While a single Representative for a geographical area may speak from the overall consensus position, a House of three elected by Meek-STV from that same area will have dissenting opinions as if the voters were sliced into their distinct ideological groupings and given a chance to elect their own representation on that basis rather than on simple geographical proximity. These representatives raise new ideas and concerns more-readily because of their greater deviation from the overall consensus.
The Representative Senate and Executive
If the House represents proportional ideology of the governed, then the Senate—and any other single-representative offices, such as Mayors, Governors, City Council members, and Presidents—must represent an overall consensus. These elect by Condorcet methods, such as Tideman’s Alternative.
The Senate typically represents a geographical area, such as a City Council district, a Legislative district, or a State. While the House leads with new ideas, the Senate represents a whole, balanced view. In a more-progressive district, a Senator will be more-progressive, while sending to the House a highly-progressive voice outside the normal bounds of the political dialogue. A more-conservative district will tend to elect a more-conservative Senator, yet may also send both a liberal and a far-more-extreme conservative to represent its constituency in the House.
Likewise, an Executive office such as a President, Governor, or Mayor must consider in their duty the will of the people as a whole. As the minds of the people shift, so too will the Executive—and the Senate—to fully represent their constituencies.
Local Councils tend to use a single house, elected as a Senate. While the House usually carries more representation than a Senate, a local Council may invert this for a bicameral structure: a City may elect its Council Senate geographically by Condorcet methods, and then carry out a Citywide election to select perhaps one in the Council House per Senator. A City of thirteen to fifteen districts, for example, may elect five to the Council House via Meek-STV.