The question itself is ambiguous enough to distract from its actual implications. Let's dissect it into three parts:
- "Should citizens give up"
- "some of their privacy"
- "in return for greater security?"
The first part is important here. "Give up" implies that privacy is something one owns as an extension of the self, rather than a privilege that may be revoked. That is, the right to spatial or intellectual privacy is something inherent to self autonomy, i.e. freedom from interference or unwanted proximal contact with an external body. The opening "should" implies consent. But if privacy is inherent to self autonomy, then consent can only be given on an individual basis, not by any collective democratic decision. The argument often presented by the other side - "if you have done nothing wrong, you have nothing to hide" - falls apart on this basis, because, of course, if you have something to hide, you aren't going to consent. Considering this, one sees this opening section as redundant; we are not actually being asked to give up our privacy - we are being asked whether or not to object to its blanket violation for a common good. One must ask, then, what exact violation we are choosing to object to.. which leads me nicely on to...
the second part. What exactly is "some of their privacy" in this context? According to kem_pel, a supporter of the Yes side, the realms of monitoring are not focused on the individual, but upon certain spatial domains, such as "unindexed material" like child pornography websites. His suggestion can be simplified thus: if you walk into the path of a CCTV camera, you forfeit the privacy of your actions within that space. Indeed, certain domains must be monitored in order to keep track of criminal behaviour, and those who enter these domains forfeit their right to privacy by doing so. But this is not what is being requested. Read: citizens / their privacy... we are not being asked to forfeit privacy in certain domains. We are being asked, as previously, whether we object to the violation of our personal privacy, an inherent right as an extension of personal autonomy. As a continuation of the metaphor, this is tantamount to having a CCTV camera installed upon our forehead. In practice, this could include, and is not limited to the monitoring of: all online communications and browsing activity, phonecalls and texts, card transactions, personal affiliations with people and groups... and so on. Obviously, "some" is not specified here, but suffice to say that justification for "some" can as easily be justification for much or all, depending on what purpose you are collecting this data for... which leads me finally to...
the third part. This part is almost irrelevant. If the purpose of collection is general security (with no specified threat), if just one person objects to the blanket surveillance this entails, that surveillance is rendered illegitimate. If the purpose of collection is specific, targetting domains (kem_pel's "unindexed materials", for example) is more effective and less intrusive a method than the blanket monitoring or recording implicit in the question. What domains are legitimate for state monitoring is a separate debate.
The conclusion here is a rewording of a misleading question, argued for on the Yes side by irrelevant points. The rewording is thus: Should an individual accept any measure of personal surveillance of their actions by the state under any circumstance? The answer, obviously, is no.