A civilization is any society characterized by the emergence of complex systems on top of the more basic cultural traits of a linguistic tradition, religious-ethical codes, and agricultural sedentarism. Namely: a writing system, a legal system, governments and urbanization (Haviland et al., 2013; Fernández-Armesto, 2001; Boyden, 2004; Solms-Laubach, 2007; Abdel-Rahim, 2015).
The Western Civilization Index captures exactly those traits, defines criteria for each of them, and then evaluates countries according to these criteria.
The total country score is simply the average over all civilizational traits, expressed as a percentage.
Language: Romance or Hellenic language majority. Half a point awarded if at least 33% of the population speaks them.
We have started from a seed of core languages upon which the Western literary and philosophical tradition is based: Greek and Latin. The next step is to consider closely related languages, and linguistic philogeny reveals that Greek is in fact closer to Armenian and Albanian than it is to Latin, and that Latin is as close to Greek as it is to Persian and Sanskrit. Since the whole Indo-European family is evidently too wide for Western culture, and since there's no objective linguistic reason to accept Germanic, Celtic or Slavic languages above something like Armenian or Sanskrit, we have stopped at Hellenic and Romance languages. Similarly, the writing traditions associated with other Indo-European branches, such as Germanic runes, have had no lasting impact on Western civilization.
Writing: Predominance of Latin, Greek or derived (e.g. Cyrillic) script, used as an alphabet proper (phonetic writing).
If used more as an abjad or logograms (as in contemporary English), we consider it as defeating the purpose of the alphabet, and only award half a point, for pedigree. If the script is eminently phonetic but comes from a different tradition (as in Korean hangul or Indian devangari), we also recognize the analogy with half a point.
Law: The clear contender for a Western legal system is so-called Civil Law, which traces its roots to Roman law, and was later influenced by Enlightenment reforms, which spread to many parts of the world via the Napoleonic code. Half a point is awarded when Civil Law is mixed with at most one different legal system (for instance, Civil Law mixed with Chinese customs)
By contrast, Anglosaxon law (Common Law) has an origin as different from Roman-Napoleonic law as something like Sharia law. Since there's no objective reason, following legal history and comparative studies, to include Common Law but not Sharia or some other customary law, we don't include them in the Western tradition.
Democracy: A full point is awarded if, roughly speaking, the country has tended towards democratic forms of government (any kind of democracy, parliamentary monarchy included) over the last few decades; as measured for instance by different democracy indices. Half a point awarded for flawed or developing democracies.
Although not exclusive to the West, and although radically different from its original incarnation, this form of government advanced by Athens and sometimes adopted by Rome forms the basis of Western governance. While largely abandoned during the European Middle Ages, the Enlightenment brought a resurgence of democratic forms of government that still persist to this day.
Religion: Catholic or Orthodox historical background, or outright majority in the present. Half a point awarded for a minimum of 33% of the population.
Following our methodology, this combination turned out to be the most principled criterion. We obviously want to avoid religious sectarism by limiting Western culture to a single branch of Christianity. While a "Catholic or Protestant" ticket sounds like the obvious choice from a geographical perspective, an objective cultural analysis reveals that such a pair doesn't minimize cultural dissonance, generally speaking. Moreover, Protestantism is an umbrella term for widely differing Christian religions.
By contrast, although the schism between Eastern Orthodoxy and Catholicism is much older, both traditions remain closer to one another, for instance in terms or rituals, theology, their preference for communitary values, and even in architectural choices. The fact that one is called "Eastern" is about as consequential as the name "Democratic Republic" in making North Korea a democracy.
Urbanism: Predominantly built in masonry, with an emphasis on public architecture, as received from the Greco-Roman urbanistic style which is eminently characterized by agoras, forums and the more recent variants: squares and plazas.
Half a point is awarded if at most one of the following is missing: Majority of constructions built in masonry (e.g. not wood). Public architecture about as prevalent as in, say, Italy or Spain. Prevalence of European styles (e.g. not Mesopotamian, Khmer or Tiwanaku).