The numbered topic headings are links.
1. The number of politicians is the cube root of the population - in all kinds of political regimes and in large collectives.
Taagepera and Shugart's Seats and Votes (1989) give confirming statistics around the world and also manage to deduce it theoretically. They assume a politician's job is to maintain contact with both constituents and other politicians. Then they assume pollies want to minimise their workload and with a touch of differential calculus they show the optimum number of pollies is the cube root of twice the voters.
It fits within plus or minus 50% practically everywhere, democratic or otherwise. It even applies to large organisations like unions. 50% may sound loose but for an empirical fact of mass behaviour it is remarkable.
Naive writers often look at simple ratios but it should be obvious that China could not have the sort of ratio of representatives to population of, say, Australia.
2. Autocracy (dictatorship, one-party government) is not stable.
In the last twenty years this has become a mundane assertion. Dictatorship may be stable enough in the short term to satisfy the dictator or the foreign corporation on whose behalf it is installed, e.g., British oil companies in Iran; United Fruit's banana monopoly in Guatemala. A dictator - Shah in Iran, Pinochet in Chile - breeds present and future trouble for the country (and for all who must deal with it) if not for the dictator or the corporation.
Concentration of power is always a disaster.
3. Stability comes from incorporating a diverse range of opinions and attitudes into the ruling structure. Verbal dissension is needed to obviate violence.
Switzerland and Northern Ireland are outstanding positive and negative examples of stability in diversity. Switzerland has three languages and two major religions and everyone gets a say. It has one of the world's highest per capita incomes, outstanding environmental policies and by far the world's most successful foreign relations. In NI the Protestant power monopoly caused civil war after fifty years. The proportional representation (PR) electoral system introduced in the early 1990s allowed both religions to win seats and the civil war came to a halt.
4. Democracy is rule by the people. A perfect democracy is where everyone has a precisely equal say in making the rules. Democracy is not an attitude, not a voting procedure, not an institutional arrangement. Democracy is a matter of degree. Procedures and institutions are democratic to the degree they allow or enable rule by the people.
Some think democracy requires a "democratic attitude" but there is no evidence. Institutions thought to be democratic might not be. For example, in 1963 adult franchise was extended to the upper house of Western Australia but it was antidemocratic for it cemented one-party rule. A citizen initiated referendum system could be antidemocratic if it gave more power to big corporations rather than to the people - for example by having such stringent petition requirements that only the wealthy could initiate a referendum.
Whatever gives the people more leverage over political decisions is more democratic.
5. Democratisation and extensions of democracy occur as a by-product of intra-elite struggle, the hand-over of power being regretted by the politicians who reluctantly relinquish it to the people as a means of keeping it from rival politicians.
Politicians are professional power brokers whose life's work is to acquire and wield power. Typically, they fight tooth and nail to get it and to keep it, and they give it away voluntarily only through old age - and then often to their own offspring. Political parties never give away power willingly.
Elites may relinquish political power for money but the only circumstances where they give up power to the people is when it will bring them an advantage over rival elites, i.e., when collusion with the rivals (to take or keep power from the people) has broken down.
The situation must be that they have an opportunity to take some modicum of power from their rivals but they cannot grab it for themselves so rather than leave it with their rivals, they let it devolve to the people. The elites will be aware their action is democratic and may boast of it but the chest-thumping is hypocrisy: they are doing it in order to get one up on rival elites, not to extend democracy.
Around the world this seems to be the process by which hundreds of gerrymanders and other political fiddles have been rectified over the last 150 years. The action is never the result of public activism and the general public is usually unaware it has gained additional power.
6. Democracy cannot exist without a free market.
After the horrors of the Soviet Union, Mao's China and Pol Pot's Cambodia, this is no longer worth debating. Tendencies of the free market to bribe and bully just have to be regulated.
7. Democracies never war against each other.
True even for half-baked democracies. This must be the most nearly perfect law in all social science. First noticed in the 1950s or 60s it finally surmounted conservative prejudice and became widely known in the 1990s. The policy consequences are clear: when all countries are democratic, war will no longer exist. An extensive Wikipedia article on this "democratic peace" examines virtually every war there ever was.
8. Democracy requires regular elections.
Elections are the basic provider of power to the people. Holding regular (fair) elections is the sine qua non of democracy. The people's effort is to mark a ballot paper once every few years; it may seem very little but it is crucial.
9. Representative democracy requires more or less regular changes of government, i.e., of ruling representatives.
Too much stability is bad. Changes of government demonstrate that elections (and the system generally) are fair. In a "majoritarian" system (where each electoral district elects only one representative) the government has to switch otherwise some voters will be permanently excluded from influence (which isn't democratic - Northern Ireland was stable for fifty years before it blew up). In a PR system with shifting coalitions, it is more subtle because government is usually a coalition. Japan, a PR system, had no significant change from 1955 to 2009 and is not very democratic.
10. Direct democracy does not require regular change of government.
Switzerland has municipal, cantonal and federal elected representatives but legislation is subject also to direct referendum. The government has not really changed since the 19th century and the party composition of the federal cabinet has not changed since 1943. With very rare exceptions, ministers stay in the job until they have had enough of it. No minister is concerned about not being re-elected due to poor management or policies.
11. Democracy does not require a "loyal opposition" as an alternative "government in waiting."
This is ethnocentric Westminster myth. It is a consequence of "majoritarian" electoral systems, not a general requirement of democracy. Where electorates are single-member, an election is a winner-take-all competition and will usually be between two parties (because third parties can get no purchase). The result is that one party wins and the other loses so about half the people have no influence in the parliament. Therefore, if the polity is to be democratic, the two sides must take turns in power. Hence the evolution of - the perceived need for - a "government in waiting" complete with "shadow ministers." In presidential US and in much of parliamentary Europe there is no such thing. In semi-presidential Switzerland it is the people who form the opposition.
12. With a proportional representation (PR) electoral system, no second chamber ("upper house") is needed.
With a PR house a second chamber is superfluous except in federations. Lijphart in "Patterns of Democracy" (1999) lists eleven national unicameral PR parliaments. Thus no harm was done when the upper houses of Denmark, Sweden and Bavaria were abolished. The Tasmanian upper house could be abolished and probably should be. The lower houses of Australia, NSW, SA, WA, and Victoria could not be abolished because they form the government. However, since they always defer to the legislation of the PR upper house, their sittings are superfluous and could (and should) cease.
13. A second chamber is essential if the government is formed from a majoritarian (i.e., single member electorates) parliament.
In a single-member system a single party usually holds the majority so the house is its creature. Northern Ireland is the most notorious example of the poison that is a majoritarian single chamber; NZ tried it and quickly abandoned its Westminster tradition for West German PR. Papua New Guinea, Vanuatu and the Solomon Islands have all failed and are propped up by, and in thrall to, Australia. They will never succeed. Mauritius failed and is now modified majoritarian (3-member seats, seats reserved for minorities). Sub-national unicameral majoritarian single chambers such as Queensland, Northern Territory and the Canadian provinces can function by being restrained and jerked into line by the federation.
The two hundred year-old question, "What is the use of an upper house?" does have one answer: where there is a majoritarian lower house, a second chamber is needed to inhibit government corruption. Even the most wretchedly undemocratic upper house, as in the UK and Canada, is better than none when the lower is formed from single-member electorates.
14. For genuine debate, no party may hold a house majority. The only electoral scheme that can hope to ensure no party wins a majority is PR. Hence an upper house which is to keep the lower house honest must be PR.
An upper house with a single party majority will be either compliant or obstructionist depending on whether the party is in government or in opposition. Lijphart (e.g. 1999) says the upper house electoral basis should be different from the lower house but what matters seems to be that it must represent interests, rather than the people and the geographic areas which the majoritarian lower house represents. Thus it might represent property or aristocracy or, if PR (the only modern possibility), ideologies. Appointing the House of Lords is a solution which only the stubbornly anti-democratic English would nowadays agree with.
15. Where there is a majoritarian lower house, ministers should not be permitted in the upper house.
This is often suggested. It would eliminate ministerial ambition from upper house members. Members would dream of good legislation, rather than a chauffeured limousine. This would foster independence, house loyalty, committee prestige, and good law.
16. A federation presumably requires a second chamber.
A "states' house" seems to be necessary though it may be just for show. All the federations except a couple of microscopic Caribbean ones do have second chambers. In Germany the upper house seems to represent states but in the other strong federations - Australia, Canada, Switzerland, US - it generally doesn't and the house is just another legislative chamber.
In Switzerland the people at referendum form, in effect, a third chamber.
17. A federal structure is essential if there are deep cleavages within the nation.
Federalism is the compromise which makes it possible to form a nation from a divided society. The USA, Switzerland and Belgium are prime examples. Iraq would have to be.
18. In a federation, the states must have recourse against the federal government. This usually requires an unbiased constitutional court.
If the states cannot take on the feds legally then power will gravitate to the centre. The Swiss constitutional court is not permitted to express an opinion on federal law. There, referendums curb federal power accretion. What prospect in Iraq of an unbiased court?
19. Unitary (not-federal) countries do not seem to need a court with power to rule on the constitutionality of legislation.
In Holland the court cannot pass judgement on a law. Britain also has no court which can check parliamentary power.
20. Presidential government (i.e., where the executive does not need to hold the "confidence" of the legislature) is not viable.
There is only one country where the presidential system sort of works. It failed in the Philippines, failed in South Korea, failed time and time again in Latin America. It is now failing in the former Soviet Union and other former Soviet countries. Evidently, for representative democracy the executive must be answerable to parliament.
Perhaps the "division of powers" among the states keeps the US from turning into a dictatorship. Also, the president's own power is based in a state. In semi-presidential Switzerland, though the cabinet is elected by parliamentarians from among their number, ongoing "confidence" is not required. Instead, referendums limit executive power.
2017 update. Trump's power is not based in a state. He had no formal political power until his election. The US has always staggered and lurched, going nuts every now and again (robber baron capitalism, great depression, sterilisation programs, McCarthyism) and it is now having another turn. As someone said, if the rich don't throw the peasants enough crumbs, they will come with their pitchforks.
Presidential systems are, world-wide, a disaster. Right now, Turkey is headed for tragedy.