Short answer: This is mostly a question about statistical significance.
Cognitive dissonance theory encompasses several different research paradigms. I believe this question is about the "free-choice" paradigm - the only one that involves decision-making. This paradigm is also sometimes referred to as "choice-induced dissonance", or "post-decisional attitude change" (though the latter may be a misnomer, as attitude change may happen during the decision-making process rather than after).
In the original formulation of this paradigm by Brehm (1956):
A second prediction, that dissonance and consequent attempts to reduce
it would be greater, the more closely the alternatives approached
equality, also received support.
That is, it was suggested that dissonance occurs in all decisions, but decisions arouse more dissonance the more difficult (closer) they are, and presumably less dissonance the easier (more distanced) they are. The problem with this formulation is that at some point, the dissonance induced by sufficiently easy decisions is so small as to fail to reach statistical significance (p-value), making it essentially impossible to test this aspect of the hypothesis.
In the first 50 years or so since the theory was proposed, much support has been found for dissonance aroused by difficult decisions (for reviews, see Cummings & Venkatesan, 1976; and Harmon-Jones & Mills, 1999). Numerous variables other than "closeness of alternatives" have been proposed to moderate dissonance, such as importance of the decision, relevance to self, how public the decision is, personality traits, etc - see Kenworthy et al (2011) for a review.
Then, Chen and Risen (2010) called the entire paradigm into question by pointing out that it is subject to a statistical artifact (first noted in 2008) that could be responsible for many false-positive results. That is, statistically significant changes in preference may be even more difficult to induce in subjects than previously believed.
Researchers are currently in the process of replicating and reevaluating the body of work that this paradigm is based on, controlling for the statistical artifact. Unfortunately, any assessments made prior to this of the level of cognitive dissonance produced by decisions are likely overestimated:
Using the free-choice paradigm, many social psychological studies have
investigated the effect of moderating factors on choice-induced
preference change ... (e.g., choice importance, choice reversibility,
etc. ...) ... However, without a proper control condition, any
argument about absolute preference change would not be warranted
(i.e., it is unclear whether or not significant dissonance reduction
occurred in each condition). ...
The same argument applies to past studies comparing preference change
between two groups of individuals with different personalities ... or
different cultural backgrounds ...
Data from Izuma et al. (2010) suggests that individual differences in
preference changes, which are measured in the typical free-choice
paradigm explain only about 28% of the total variance in true