Classification accuracy based on top 3 most likely classifications My goal is to recommend jobs to job seekers based on their skill set.

Currently I'm using an SVM for this, which is outputting one prediction, e.g. "software engineer at Microsoft". However, consider this: how significantly different are the skill sets of a software engineer at Microsoft and a software engineer at IBM? Probably not significantly different. Indeed, by inspection of my data set I can confirm this. Hence, the SVM struggles to discriminate in situations like this, of which there are many in my data set, and my classification accuracy is about 50%.

So I had an idea.

In SK Learn, once you've trained some model, you can compute the probability a particular input X belongs to each class.

So for each input X in my test set, I took the the top 3 most likely classifications. Then I tested whether or not the correct label was in the top 3 predictions. If it was, then I considered the prediction to be correct. In doing so, the classification accuracy increased to over 80%.

So my question is: is this a valid approach to measuring classification accuracy? If it is, then does it have a name?

In my mind, it is valid given my intended application, which is to recommend a selection of jobs to a job seeker, which are relevant to their skill set.
This is called top-3 accuracy.  See https://stats.stackexchange.com/q/95391/2921, https://stackoverflow.com/q/37668902/781723, https://stats.stackexchange.com/q/156471/2921.  Sure, you can use it.  Whether top-1 accuracy or top-3 accuracy is better correlated with user satisfaction will depend on your particular application and on your users.