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  1. You are actually the third person to call with the same issue.
  2. You are actually the third person to have called with the same issue.
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In both sentences the role of the infinitive is to qualify person: its purpose is to identify a particular type of person. A relative clause could be used to produce the same effect:

You are actually the third person who has called with the same issue.

The first sentence uses the present infinitive to call, which can be used about a single action, a repeated action, a continuous action or a state.

I want to press the button! - single action.
He seems to know - state

The second sentence uses the perfect infinitive, which indicates that something has been or will be completed.

He is the first person to have crossed the Atlantic in a bathtub - past
He will be the first person to have crossed the Atlantic in a bathtub - future

Neither type of infinitive gives any indication of timescale (past, present, future): that is provided by the context.

John wanted to press the button - past
John likes to press the button - general truth
John wants to press the button - future

You can regard a call either as the action of picking up the phone and dialling the number, or as the entire process, including the conversation and hanging up. If the speaker views the call as just picking up and dialling, then part-way through the phone call the speaker could use present infinitive (calling is a single action) or perfect infinitive (completed action).

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Honestly, at an intuitive level, it sounds fine to me both ways, with #1 sounding perhaps a little more natural and #2 sounding a bit more formal or stilted (which, on further investigation is probably because the second construction is often used in passive sentences, which tend to sound more formal).

That said, hopefully I can help you in researching this. The distinction between #1 and #2 is that #1 uses a to infinitive (to call), while #2 uses a perfect infinitive (to have called). So the abstract question you're interested in is: What is the usage or distinct meaning of the perfect infinitive?.

In general, the perfect infinitive is used to discuss uncertain ideas, such as reported speech or beliefs/expectations about the past.

For example:

  • He seems to have contracted a bad flu. (inference about the past)
  • Mammoths are said to have once wandered the plains of Illinois. (reported speech about the past)
  • She expects to have earned her PhD by 2020. (an expectation about the past from the perspective of 2020)

So, very strictly speaking, #1 would be more in line with documented native usage of English because there is no uncertainty about the past callers ('actually' clarifies this is a fact, not speculation). But again, if I heard this in a daily conversation, it would not seem particularly strange to hear #2.

Do take a look through source #1 for quick coverage of the basics of this construction.

  • Also, see @JavaLatte's answer above about completed actions, as the perfect infinitive is also used to show completion as they describe. I do still feel that #1 sounds ever slightly more natural though. – David Bodow Jan 21 '18 at 3:43

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