Comparative Authoritarianism vs Authoritarianism

Okay, so this is in relation to the article 'Rise of Competitive Authoritarianism' which we discussed in my tutorial today. So theoretically, competitive elections in an authoritarian regime would open it up for another political party to win the election, and take over.

This would indicate that weaker authoritarian states are more likely to have elections, as they are too weak to make the transition to a full authoritarian state.

This, I'm pretty sure, is what Levitsky and Way conclude in their article.

Now, I am wondering why a competitive authoritarian state

is not more desirable to authoritarian leaders than an outright authoritarian one?

Okay granted, they have elections which means competition and a possibility of losing power. Though in reality, these elections are so corrupt, For example,

-Gangs forcing people to vote a certain way and/or having a biased media,

so the threat of losing an election is rather erroneous.

Insofar as I am concerned the benefits for an authoritarian dictator to have elections, and, again, for example, legitimising one's own position of power nationally, and internationally - shockingly outweighs the benefits of having a democratic disguise when trading with other democratic countries.

All seem to me to outweigh the slightest possibility of losing an election, especially considering the coercion involved.

So why are comparative authoritarian regimes restricted or most popular in weak states?

Why are holding so-called 'democratic' elections, when they are still holding fast to the idea that they may in fact be holding the election of the opposite ideal?