A dictionary definition.

Democracy: government by the people; a form of government in which the supreme power is vested in the people and exercised directly by them or by their elected agents under a free electoral system.

The problem is that such textbook definitions don't take into account the many ways democracy can be imperfect. I'm aiming at a more realistic measure.

Citizenship

A democracy must allow all "citizens" to vote. In addition it must not restrict the definition of citizenship is such a way as to exclude various disfavored groups. For example some countries exclude permanent resident populations who are not members of the dominant ethnic group. There should also be a straightforward way for new residents to obtain citizenship within a reasonable period of time.

Democracies should also not remove the right to vote from citizens, except in very limited cases. Mental incapacity seems appropriate, imprisonment or former imprisonment not as much. Societies regard removing the right to vote as part of the "punishment" of law breakers, but as these people are still affected by the actions of the government they should still have some say in how their lives are regulated.

Other qualifications such as literacy, land holdings, income, or relocation within a country should also not be used to restrict the right to vote. A change of domicile should only restrict voting rights for the time it takes to process the change of address. With modern computer systems this should be at most one month. Fears about people changing location just to vote are unfounded.

Voting

Having established who can vote, the next criterion is as to how the votes are counted. For example, having unequal district sizes for the selection of representatives means that some votes are worth more than others. Winner-take-all, rather than proportional assignment of officials, also acts to effectively disenfranchise people. Various forms of Gerrymandering can be used so that minority votes are diluted in such a way that the group never gets any representation. Conversely they may all be grouped together so that the group have little influence outside of a limited number of districts.

In addition to "legal" policies which dilute votes there are many corrupt practices which exist. Such steps as vote rigging, intimidation of voters, restricting the candidates who can stand for office on various trumped up charges, and control of the media are also common. NGO's which monitor elections to see if they are fair issue reports, but even the most damning report doesn't prevent the corrupt officials from taking power anyway. The increase in the cost of running a campaign in the era of corporate media has disfavored candidates without access to financial resources. This relationship taints the legislative process which I discuss next.

Legislation

Every democracy has some sort of separation between an executive and a legislative function. A government where the people elect a chief executive who then rules by decree is not a democratic government. There is no feedback mechanism to influence the policies that are enacted. This means that there are various bodies dedicated to creating legislation. Once these representatives are chosen one needs to consider how their agenda is chosen and what the basis is for their support of pending legislation. In many countries the parties control their members. The party leadership determines the party's position and the members just follow instructions. This is not very democratic as the voters have no input.

Another common occurrence is to have legislators beholding to those who funded their campaigns. Even in the US we have had individuals tagged as "the senator from Boeing" or "Wall Street". This goes beyond looking after the interests of big firms in one's district, since the firms did not vote and their interests may not coincide with those of the majority of the citizens in the district. In states where voting tends to follow along ethnic lines a legislator of one group rarely looks after the interests of other groups even when there are such citizens within the district.

Many nations have more than one legislative body; the US has the Senate and the UK the House of Lords. These are usually very undemocratic. The US senate gives much more weight to states with small populations. In fact 18% of the population controls 50% of the votes. The House of Lords (until recently) had no pretensions to being democratic at all. There may be a benefit to having a more deliberative body, but it still needs to reflect the makeup of the population.

Judiciary

Once laws are passed they need to be interpreted. In addition, violations of them need to be enforced. A functional democracy needs an impartial, independent, yet responsive judiciary. There have been many attempts to make the selection of judges more democratic, but most have produced ambiguous results. Appointing judges for life is supposed to ensure that they are not beholding to special interests, but being free of outside influence once on the bench doesn't mean that one doesn't bring one's prejudices and loyalties along. This is so well known that most lawyers try to do judge shopping if they have an opportunity. The number of cases that are reversed on appeal shows that the decision-making process remains flawed. Clear laws would not be open to such widely varying interpretation.

Executive

In general the executive branch is meant to carry out the laws which have been enacted. In some societies the executive proposes new legislation, while in others it is the legislature which does this. Whatever the formal mechanism, in practice the executive usually sets the agenda. The various agencies and departments of the executive branch are not chosen democratically, but are some combination of political patronage and formal civil service selection rules. In some countries (France is often quoted in this respect) civil servants are seen as a quasi-independent branch which continues on its way as executives come and go. This may help prevent chaos when control passes from one majority to another with sharply opposing political philosophies. The history of nationalization in the UK is a case in point. Stability comes at a price, however. There is no mechanism for the people to alter the function of the permanent civil service.

In the US the courts have ruled that the winning party has an explicit right to fill patronage jobs in executive agencies. Sometimes these are just paybacks to supporters - ambassadorial posts are a favorite, but increasingly the posts have been filled by ideological hacks with no expertise in the area under their supervision. There has also been a proliferation of new titles meant to avoid the limits on the number of such patronage jobs available. This has made agencies more political and less impartial. Other steps have been taken to prevent legislation on the books from being enforced. This includes leaving key seats open so that agencies don't have a quorum, refusing to prosecute or investigate possible violations of laws and tinkering with the funding of agencies whose purpose is at odds with the prevailing political philosophy.

In many countries it is necessary to bribe agency workers if one is to get action on routine matters that come before them. This can range from the petty, like getting a visa, to the awarding of million dollar contracts. Even legislators are frequent recipients of bribes in some nations. Money destroys representative democracy.

Other Organizations

These days the primary non-governmental organization is the for-profit enterprise. Even nominally "communist" states like China are increasingly replacing state-owned firms with private ones. In the classic model a public firm sells shares to investors who then have a voting interest in how the firm is managed. Over the past 100 years this link has become increasingly tenuous as ownership becomes more diffuse and as firms are increasingly run by a professional managerial class which has little connection with the founding or long-term survival of the firm. Managing is seen as a skill and, apparently, the same person can sell sugar water or computers equally well. Compensation packages for the managerial class are designed in such a way that they are mostly insulated from the results of their actions. Terms like "golden parachute" show that even the worst manager can expect to leave richer than when he arrived. The selection of the top management and the board of directors is far removed from the control of the shareholders. In the US one sees fewer than a dozen attempts by shareholders each year to change control of large firms. Even with this small number, many fail.

Firms have a  non-democratic, self perpetuating management structure, where investors, employees, customers and suppliers have no meaningful influence on policies. Even when one of these interest groups has some success in promoting its interests the mechanism used is not a democratic one, but raw economic power.

In addition to public firms there are a variety of quasi-public organizations. Charities, NGO's, educational intuitions, religious organizations and the like are never organized along democratic lines. Most are run by self selected boards, and when there are nominal elections for the board seats, it is extremely rare to see more than one candidate for each seat. Nomination processes are arcane or non-existent. As most of these quasi-public organizations get tax breaks or other public benefits, the citizens end up funding them in part while having no say on what the mandates of these groups are.

Conclusion

True democracies perform better for the bulk of the population. That this needs to even be stated, shows how far simple truisms can be distorted by the powerful. When the people have control they are not going to support policies that are harmful to themselves. This doesn't mean that everything will always turn out for the best. People can make mistakes. They can be uninformed, overly cautious, or unable to predict the future properly, but at least the mistakes are their own. Democracies can also suffer from the "tyranny of the majority", but then I would rate them as imperfect, just another defect to add to the lists above.

So, those who want to prove this correlation need to take all the imperfections into account when measuring the real status of democracy in a country and look beyond the nominal measures. By these criteria some of the world's "best" democracies fall far short. If the populations in these states fail to realize this then, perhaps, they deserve the fates awaiting them. Remember no state can exist without the acquiescence of the governed. It is allowing oneself to be dominated by institutions that makes democracy fail. The Philippines was a good example of how a dictatorship could be ended (Markos) when the population just stopped participating in society. Others can do the same, but it requires a willingness to take a risk and sacrifice some temporary security. It doesn't require violent revolution.