Graded Relevance

NTCIR was the ﬁrst large-scale IR evaluation conference series to construct test collections with graded relevance assessments: the NTCIR-1 test collections from 1998 already featured relevant and partially relevant documents. In this chapter, I provide a survey on the use of graded relevance assessments and of graded relevance measures in the past NTCIR tasks which primarily tackled ranked retrieval. My survey shows that the majority of the past tasks fully utilised graded relevance by means of graded evaluation measures, but not all of them; interestingly, even a few relatively recent tasks chose to adhere to binary relevance measures. I conclude the chapter by a summary of my survey in table form.


Introduction
The evolution of NTCIR is quite different from that of TREC when it comes to how relevance assessments have been collected and utilised. In 1992, TREC started off with a high-recall task (i.e., the adhoc track), with binary relevance assessments (Harman 2005). Moreover, early TREC tracks heavily relied on evaluation measures based on binary relevance such as 11-point Average Precision, R-precision, and (noninterpolated) Average Precision. It was in the TREC 2000 (a.k.a. TREC-9) Main Web task that 3-point graded relevance assessments were introduced, based on feedback from web search engine companies at that time Hawking and Craswell (2005, p. 204). Accordingly, this task also Järvelin and Kekäläinen (2000) adopted Discounted Cumulative Gain (DCG), to utilise the graded relevance assessments.
NTCIR has collected graded relevance assessments from the very beginning: the NTCIR-1 test collections from 1998 already featured relevant and partially relevant documents . Thus, while NTCIR borrowed many ideas from TREC when it was launched in the late 1990s, its policy regarding relevance assessments seems to have followed the paths of Cranfield II (which had 5-point relevance levels) Cleverdon et al. (1966, p. 21), Oregon Health Sciences University's MED-LINE Data Collection (OHSUMED) (which had 3-point relevance levels) (Hersh et al. 1994), as well as the first Japanese IR test collections BMIR-J1 and BMIR-J2 (which also had 3-point relevance levels) (Sakai et al. 1999).
Interestingly, with perhaps a notable exception of the aforementioned TREC 2000 Main Web Task, it is true for both TREC and NTCIR that the introduction of graded relevance assessments did not necessarily mean immediate adoption of evaluation measures that can utilise graded relevance. For example, while the TREC 2003-2005 robust tracks constructed adhoc IR test collections with 3-point graded relevance assessments, they adhered to binary relevance measures such as Average Precision (AP). Similarly, as I shall discuss in this chapter, 1 while almost all of the past IR tasks of NTCIR had graded relevance assessments, not all of them fully utilised them by means of graded relevance measures. This is the case despite the fact that a graded relevance measure called the normalised sliding ratio (NSR) 2 was proposed in 1968 (Pollock 1968), and was discussed in an 1997 book by Korfhage along with another graded relevance measure (Korfhage 1997, p.209).

Graded Relevance Assessments, Binary Relevance Measures
This section provides an overview of NTCIR ranked retrieval tasks that did not use graded relevance evaluation measures even though they had graded relevance assessments.

Early IR and CLIR Tasks (NTCIR-1 Through -5)
The Japanese IR and (Japanese-English) crosslingual tasks of NTCIR-1 ) constructed test collections with 3-point relevance levels, but used binary relevance measures such as AP and R-precision by either treating the relevant and partially relevant documents as "relevant" or treating only the relevant documents as "relevant." However, it should be stressed at this point that using binary relevance measures with different relevance thresholds cannot serve as substitutes for a graded relevance measure that enables optimisation towards an ideal ranked list (i.e., a list of documents sorted in decreasing order of relevance levels). If partially relevant

Patent (NTCIR-3 Through-6)
The NTCIR-3 Patent Retrieval task (Iwayama et al. 2003) was a news-to-patent technical survey search task, with 4-point relevance levels. RP curves were drawn based on strict relevance and relaxed relevance.
The main task of the NTCIR-4 Patent Retrieval task (Fujii et al. 2004) was a patentto-patent invalidity search task. There were two types of relevant documents: A (a patent that can invalidate a given claim on its own) and B (a patent that can invalidate a given claim only when used with one or more other patents). For example, patents B 1 and B 2 may each be nonrelevant (as they cannot invalidate a claim individually), but if they are both retrieved, the pair should serve as one relevant document. At the evaluation step, rigid and relaxed APs were computed. Note that the aboverelaxed evaluation has a limitation: recall the aforementioned example with B 1 and B 2 , and consider a SERP that managed to return only one of them (say B 1 ). Relaxed evaluation rewards the system for returning B 1 , even though this document alone does not invalidate the claim.
The Document Retrieval subtask of the NTCIR-5 Patent Retrieval task (Fujii et al. 2005) was similar to its predecessor, but the relevant documents were determined purely based on whether and how they were actually used by a patent examiner to reject a patent application; no manual relevance assessments were conducted for this subtask. The graded relevance levels were defined as follows: A (a citation that was actually used on its own to reject a given patent application) and B (a citation that was actually used along with another one to reject a given patent application). As for the evaluation measure for Document Ranking, the organisers adhered to rigid and relaxed APs. In addition, the task organisers introduced a Passage Retrieval subtask by leveraging passage-level binary relevance assessments collected as in the NTCIR-4 Patent task: given a patent, systems were required to rank the passages from that same patent. As both single passages and groups of passages can potentially be relevant to the source patent (i.e., the passage(s) can serve as evidence to determine that the entire patent is relevant to a given claim), this poses a problem similar to the one discussed above with patents B 1 and B 2 : for example, if two passages p 1 , p 2 are relevant as a group but not individually, and if p 1 is ranked at i and p 2 is ranked at i (> i), how should the SERP of passage be evaluated? To address this, the task organisers introduced a binary relevance measure called the Combinational Relevance Score (CRS), which assumes that the user who scans the SERP must reach as far as i to view both p 1 and p 2 . 3 The Japanese Document Retrieval subtask of the NTCIR-6 Patent Retrieval task (Fujii et al. 2007) had two different sets of graded relevance assessments; the first set ("Def0" with A and B documents) was defined in the same way as in NTCIR-5; the second set ("Def1") was automatically derived from Def0 based on the International Patent Classification (IPC) codes as follows: H (the set of IPC subclasses for this cited patent has no overlap with that of the input patent), A (the set of IPC subclasses for this cited patent has some overlap with that of the input patent), and B (the set of IPC subclasses for this cited patent is identical to that of the input patent. As for the English Document Retrieval subtask, the relevance levels were also automatically determined based on IPC codes, but only two types of relevant documents (A and B) were identified, as each USPTO patent is given only one IPC code. In both subtasks, AP was computed by considering different combinations of the above relevance levels.

SpokenDoc/SpokenQuery& Doc (NTCIR-9 Through -12)
The Spoken Document Retrieval (SDR) subtask of the NTCIR-9 SpokenDoc task (Akiba et al. 2011) had two "subsubtasks": Lecture Retrieval and Passage Retrieval, where a passage is any sequence of consecutive inter-pausal units. Passage-level relevance assessments were obtained on a 3-point scale, and it appears that the lecture-level (binary) relevance was deduced from them. 4 AP was used for evaluating Lecture Retrieval, whereas variants of AP, called utterance-based (M)AP, pointwise (M)AP, and fractional (M)AP were used for evaluating Passage Retrieval. These are all binary relevance measures. The NTCIR-10 SpokenDoc-2 Spoken Content Retrieval (SCR) subtask (Akiba et al. 2013) was similar to the SDR subtask at NTCIR-9, with Lecture Retrieval and Passage Retrieval subsubtasks. Lecture Retrieval used a revised version of the NTCIR-9 SpokenDoc topic set, and its gold data does not contain graded relevance assessments 5 ; binary relevance AP was used for the evaluation. As for Passage Retrieval, a new topic set was devised, again with 3-point relevance levels. 6 The AP variants from the NTCIR-9 SDR task were used for the evaluation again. The Slide Group Segment (SGS) Retrieval subsubtask of the NTCIR-11 Spoken-Query& Doc SCR subtask involved the ranking of predefined retrieval units (i.e., SGSs), unlike the Passage Retrieval subsubtask which allows any sequence of consecutive inter-pausal units as a retrieval unit. Three-point relevance levels were used to judge the SGSs: R (relevant), P (partially relevant), and I (nonrelevant). However, binary AP was used for the evaluation after collapsing the grades to binary. As for the passage-level relevance assessments, they were derived from the SGSs labelled R or P, and were considered binary; the three AP variants were used for this subsubtask again. Segment Retrieval was continued at the NTCIR-12 SpokenQuery&Doc-2 task, again with the same 3-point relevance levels and AP as the evaluation measure.

Math/MathIR (NTCIR-10 Through -12)
In the Math Retrieval subtask of the NTCIR-10 Math Task, retrieved mathematical formulae were judged on a 3-point scale. Up to two assessors judged each formula, and initially 5-point relevance scores were devised based on the results. For example, for formulae judged by one assessor, they were given 4 points if the judged label was relevant; for those judged by two assessors, they were given 4 points if both of them gave them the relevant label. Finally, the scores were mapped to a 3-point scale: Documents with scores 4 or 3 were treated as relevant; those with 2 or 1 were treated as partially relevant; those with 0 were treated as ronrelevant. However, at the evaluation step, only binary relevance measures such as AP and Precision were computed using trec_eval, after collapsing the grades to binary. Similarly, in the Math Retrieval subtask of the NTCIR-11 Math Task (Aizawa et al. 2014), two assessors independently judged each retrieved unit on a 3-point scale, and the final relevance levels were also on a 3-point scale. If the two assessor labels were relevant/relevant or relevant/partially relevant, the final grade was relevant; if the two labels were both nonrelevant, the final grade was nonrelevant; the other combinations were considered partially relevant. As for the evaluation measures, bpref (Buckley and Voorhees 2004;Sakai 2007; was computed along with AP and Precision using trec_eval.
The NTCIR-12 MathIR task was similar to the Math Retrieval subtask of the aforementioned Math tasks. Up to four assessors judged each retrieved unit using a 3-point scale, and the individual labels were consolidated to form the final 3-point scale assessments. As for the evaluation, only Precision was computed at several cutoffs using trec_eval.
The NTCIR-11 Math (Aizawa et al. 2014) and NTCIR-12 MathIR (Zanibbi et al. 2016) overview papers suggest that one reason for adhering to binary relevance measures is that trec_eval could not handle graded relevance. On the other hand, this may not be the only reason: in the MathIR overview paper, it is reported that the organisers chose Precision because it is "simple to understand" (Zanibbi et al. 2016). Thus, some researchers indeed choose to focus on evaluation with binary relevance measures, even in the NTCIR community where we have graded relevance data by default and a tool for computing graded relevance measures is known. 7

Graded Relevance Assessments, Graded Relevance Measures
This section provides an overview of NTCIR ranked retrieval tasks that employed graded relevance evaluation measures to fully enjoy the benefit of having graded relevance assessments.

Web (NTCIR-3 Through-5)
The NTCIR-3 Web Retrieval task (Eguchi et al. 2003) was the first NTCIR task to use a graded relevance evaluation measure, namely, DCG. 8 Four-point relevance levels were used. In addition, assessors chose a very small number of "best" documents from the pools. To compute DCG, two different gain value settings were used: Rigid (3 for highly relevant, 2 for fairly relevant, 0 otherwise) and Relaxed (3 for highly relevant, 2 for fairly relevant, 1 for partially relevant, 0 otherwise). The organisers of the Web Retrieval task also defined a graded relevance evaluation measure called Weighted Reciprocal Rank (WRR), designed for navigational searches. However, what was actually used in the task was the binary relevance Reciprocal Rank (RR), with two different relevance thresholds. Therefore, this measure will be denoted "(W)RR" hereafter whenever graded relevance is not utilised. Other binary relevance measures including AP and R-precision were also used in this task. For a comparison of evaluation measures designed for navigational intents including RR, WRR, and P+, see Sakai (2007). The NTCIR-4 WEB Informational Retrieval Task ) was similar to its predecessor, with 4-point relevance levels; the evaluation measures were DCG, (W)RR, Precision, etc. On the other hand, the NTCIR-4 WEB Navigational Retrieval Task (Oyama et al. 2004 The NTCIR-5 WEB task ran the Navigational Retrieval subtask, which is basically the same as its predecessor, with 3-point relevance levels and DCG and (W)RR as the evaluation measures. For computing DCG, three gain value settings were used: . Note that the first and the third settings reduce DCG to binary relevance measures.

CLIR (NTCIR-6)
At the NTCIR-6 CLIR task, 4-point relevance levels (S,A,B,C) were used and rigid and relaxed AP scores were computed using trec_eval as before. In addition, the organisers computed "as a trial" (Kishida et al. 2007) the following graded relevance measures using their own script: nDCG (as defined originally by Järvelin and Kekäläinen 2002), Q-measure (Sakai 2014; Sakai and Zeng 2019) (or "Q"), and Kishida's generalised AP . See Sakai (2007) for a comparison of these three graded relevance measures. The CLIR organisers developed a program to compute these graded relevance measures, with the gain value setting: (S, A, B, C) = (3, 2, 1, 0).

ACLIA IR4QA (NTCIR-7 and -8)
At the NTCIR-7 Information Retrieval for Question Answering (IR4QA) task ), a predecessor of NTCIREVAL called ir4qa_eval was released (See Sect. 1.2.4). This tool was used to compute the Q-measure, the "Microsoft version" of nDCG (Sakai 2014), as well as the binary relevance AP. Microsoft nDCG (called MSnDCG in NTCIREVAL) fixes a problem with the original nDCG (See also Sect. 1.3.1): in the original nDCG, if the logarithm base is set to (say) b = 10, then discounting is not applied from ranks 1 to 10. Hence, the ranks of the relevant documents within top 10 do not matter. Microsoft nDCG avoids this problem by using 1/ log(1 + r ) as the discount factor for every rank r , but thereby loses the patience parameter b (Sakai 2014). 9 The relevance levels used were L2, L1, and L0. A linear gain value setting was used: (L2, L1, L0) = (2, 1, 0). The NTCIR-8 IR4QA task (Sakai et al. 2010) used the same evaluation methodology as above.

GeoTime (NTCIR-8 and -9)
The NTCIR-8 GeoTime task (Gey et al. 2010), which dealt with adhoc IR given "when and where"-type topics, constructed test collections with the following graded relevance levels: Fully relevant (the document answers both the "when" and "where" aspects of the topic), Partially relevant-where (the document only answers the "where" aspect of the topic), and Partially relevant-when (the document only answers the "when" aspect of the topic). The evaluation tools from the IR4QA task were used to compute (Microsoft) nDCG, Q, and AP, with a gain value of 2 for each fully relevant document and a gain value of 1 for each partially relevant one (regardless of "when" or "where") for the two graded relevance measures. 10 The NTCIR-9 GeoTime task (Gey et al. 2011) used the same evaluation methodology as above.

CQA (NTCIR-8)
The NTCIR-8 Community Question Answering (CQA) task (Sakai et al. 2010) was an answer ranking task: given a question from Yahoo! Chiebukuro (Japanese Yahoo! Answers) and the answers posted in response to that question, rank the answers by answer quality. While the Best Answers (BAs) selected by the actual questioners were already available in the Chiebukuro data, additional graded relevance assessments were obtained offline to find Good Answers (GAs), by letting four assessors independently judge each posted answer. Each assessor labelled an answer as either A (high-quality), B (medium-quality), or C (low-quality), and hence 15 different label patterns were obtained: A A A A, A A AB, . . . , BCCC, CCCC. In the official evaluation at NTCIR-8, these patterns were mapped to 4-point relevance levels: for example, A A A A and A A AB were mapped to L3-relevant, and ACCC, BCCC and CCCC were mapped to L0. In a separate study, the same data were mapped to 9point relevance levels, by giving 2 points to an A and 1 point to a B and summing up the scores for each pattern. Using the graded Good Answers data, three graded relevance measures were computed: normalised gain at l = 1 (nG@1), 11 nDCG, and Q. In addition, Hit at l = 1 was computed for both Best Answers and Good Answers data: this is a binary relevance measure which only cares whether the top-ranked item is relevant or not.

INTENT/IMine (NTCIR-9 Through 12)
The NTCIR-9 INTENT task overview paper (Song et al. 2011) was the first NTCIR overview to mention the use of the NTCIREVAL tool, which can compute various graded relevance measures for adhoc and diversified IR including Q, nDCG, and Dmeasures . D -nDCG and its components I-rec and D-nDCG were used as the official evaluation measures. The Document Retrieval (DR) subtask of the INTENT task had intentwise graded relevance assessments on a 5-point scale. While the Subtopic Mining (SM) subtask of the INTENT task also used D -nDCG to evaluate ranked lists of subtopic strings, no graded relevance assessments were involved in the SM subtask since each subtopic string either belongs to an intent (i.e., a cluster of subtopic strings) or not. Hence, the SM subtask may be considered to be outside the scope of the present survey; but see Sakai (2019) for a discussion.
The NTCIR-10 INTENT task was basically the same as its predecessor, with 5point intentwise relevance levels for the DR subtask and D -nDCG as the primary evaluation measure. However, as the intents came with informational/navigational tags, new measures called DIN-nDCG and P+Q (Sakai 2014) were used in addition to leverage this information.
The NTCIR-11 IMine task (Liu et al. 2014) was similar to the INTENT tasks, except that its SM subtask required participating systems to return a two-level hierarchy of subtopic strings. The SM subtask was evaluated using the H-measure, which combines (a) the accuracy of the hierarchy, (b) the D -nDCG score based on the ranking of the first-level subtopics, and (c) the D -nDCG score based on the ranking of the second-level subtopics. However, recall the above remark on the INTENT SM subtask: intentwise graded relevance does not come into play in this subtask. On the other hand, the IMine DR subtask was evaluated in a way similar to the INTENT DR tasks, with D -nDCG computed based on 4-point relevance levels: highly relevant, relevant, nonrelevant, and spam. The gain value setting used was: (2, 1, 0, 0). 12 The IMine task also introduced the TaskMine subtask, which requires systems to rank strings that represent subtasks of a given task (e.g., "take diet pills" in response to "lose weight."). This subtask involved graded relevance assessments. Each subtask string was judged independently by two assessors from the viewpoint of whether 11 nG@1 is often referred to as nDCG@1; however, note that neither discounting nor cumulation is applied at rank 1. 12 Kindly confirmed by task organisers Yiqun Liu and Cheng Luo in a private email communication (March 2019). the subtask is effective for achieving the input task. A 4-point per-assessor relevance scale was used, 13 with weights (3, 2, 1, 0), and final relevance levels were given as the average of the two scores, which means that a 6-point relevance scheme was adopted. The averages were used verbatim as gain values: (3.0, 2.5, 2.0, 1.5, 1.0, 0). The evaluation measure used was nDCG, but duplicates (i.e., multiple strings representing the same subtask) were not rewarded.
The Query Understanding (QU) subtask of the NTCIR-12 IMine-2 Task (Yamamoto et al. 2016), a successor of the previous SM subtasks of INTENT/IMine, required systems to return a ranked list of (subtopic, vertical) pairs (e.g., ("iPhone 6 photo", Image), ("iPhone 6 review", Web)) for a given query. The official evaluation measure, called the QU-score, is a linear combination of D -nDCG (computed as in the INTENT SM subtasks) and the V-score which measures the appropriateness of the named vertical for each subtopic string. Despite the binary relevance nature of the subtopic mining aspect of the QU subtask, it deserves to be discussed in the present survey because the V-score part relies on graded relevance assessments. To be more specific, the V-score relies on the probabilities {Pr(v|i)}, for intents {i} and verticals {v}, which are derived from 3-point scale relevance assessments: 2 (highly relevant), 1 (relevant), and 0 (nonrelevant). Hence the QU-score may be regarded as a graded relevance measure. The Vertical Incorporating (VI) subtask of the NTCIR-12 IMine-2 Task (Yamamoto et al. 2016) also used a version of D -nDCG to allow systems to embed verticals (e.g., Vertical-News, Vertical-Image) within a ranked list of document IDs for diversified search. More specifically, the organisers replaced the intentwise gain value g i (r ) at rank r in the global gain formula (Sakai 2014) with Pr(v(r )|i)g i (r ), where v(r ) is the vertical type ("Web," Vertical-News, Vertical-Image, etc.) of the document at rank r , and the vertical probability given an intent is obtained from 3-point scale relevance assessments as described above. As for the intentwise gain value g i (r ), it was also on a 3-point scale for the Web documents: 2 for highly relevant, 1 for relevant, and 0 for nonrelevant documents. Moreover, if the document at r was a vertical, the gain value was set to 2. In addition, the VI subtask collected topicwise relevance assessments on a 4-point scale: highly relevant, relevant, nonrelevant, and spam. The gain values used were: (2, 1, 0, 0). 14 As the subtask had a set of very clear, single-intent topics among their full topic set, Microsoft nDCG (rather than D -nDCG) was used for these particular topics.

RecipeSearch (NTCIR-11)
While the official evaluation results of Adhoc Recipe Search subtask of the NTCIR-11 RecipeSearch Task (Yasukawa et al. 2014) were based on binary relevance, the organisers also explored evaluation based on graded relevance: they obtained graded relevance assessments on a 3-point scale for a subset (111 topics) of the full test topic set (500 topics). 15 Microsoft nDCG was used to leverage the above data with a linear gain value setting, along with the binary AP and RR.

Temporalia (NTCIR-11 and -12)
The Temporal Information Retrieval (TIR) subtask of the NTCIR-11 Temporalia Task collected relevance assessments on a 3-point scale. Each TIR topic contained a past question, recency question, future question, and an atemporal question; participating systems were required to produce a Search Engine Result Page (SERP) for each of the above four questions. This adhoc IR task used Precision and Microsoft nDCG as the official measures, and Q for reference.
While the Temporally Diversified Retrieval (TDR) subtask of the NTCIR-12 Temporalia-2 Task was similar to the above TIR subtask, it required systems to return a fifth SERP, which covers all of the above four temporal classes. That is, this fifth SERP is a diversified SERP, where the temporal classes can be regarded as different search intents for the same topic. The relevance assessment process followed the practice of the NTCIR-11 TIR task, and the SERPs for the four questions were evaluated using nDCG. As for the diversified SERPs, they were evaluated using α-nDCG (Clarke et al. 2008) and D -nDCG.
A linear gain value setting was used in both of the above subtasks. 16

STC (NTCIR-12 Through -14)
The NTCIR-12 Short Text Conversation (STC) task (Shang et al. 2016) was a response retrieval task given a tweet (or a Chinese Weibo post). For both Chinese and Japanese subtasks, the response tweets were first labelled on a binary scale, for each of the following criteria: Coherence, Topical Relevance, Context Independence, and Non-repetitiveness. The final graded relevance levels were determined using the following mapping scheme: if Coherent AND Topically Relevant if Context-independent AND Non-repetitive RelevanceLevel = L2 else RelevanceLevel = L1 else RelevanceLevel = L0. Following the quadratic gain value setting often used for web search evaluation (Burges et al. 2005) and for computing ERR (Chapelle et al. 2009), the Chinese subtask organisers mapped the L2, L1, and L0 relevance levels to the following gain values: 2 2 − 1 = 3, 2 1 − 1 = 1, 2 0 − 1 = 0; according to the present survey of NTCIR retrieval tasks, this is the only case where a quadratic gain value setting was used instead of the linear one. The evaluation measures used for this subtask were nG@1, P+, and normalised ERR (nERR). As for the Japanese subtask which used Japanese Twitter data, the same mapping scheme was applied, but the scores ((L2, L1, L0) = (2, 1, 0)) from 10 assessors were averaged to determine the final gain values; a binary relevance, set-retrieval accuracy measure was used instead of P+, along with nG@1 and nERR.
The NTCIR-13 STC task (Shang et al. 2017) was similar to its predecessor, although systems were allowed to generate responses instead of retrieving existing tweets. In the Chinese subtask, 7-point relevance levels were obtained by summing up the assessor scores, and a linear gain value setting was used to compute nG@1, P+, and nERR. In addition, an alternative approach to consolidating the assessor scores was explored, by considering the fact that some tweets receive unanimous ratings while others do not even if they are the same in terms of the sum of assessor scores (Sakai 2017). The NTCIR-13 STC Japanese subtask used Yahoo! News Comments data instead of Japanese Twitter data. The evaluation method was similar to what was used in the previous Japanese subtask; see Sakai (2019) for more details.
Although the Chinese Emotional Conversation Generation (CECG) subtask of the NTCIR-14 STC subtask (Zhang and Huang 2019) is not exactly a ranked retrieval task, we discuss it here as it is a successor of the previous Chinese STC subtasks that utilises graded relevance measures. Given an input tweet and an emotional category such as Happiness and Sadness, participating systems for this subtask were required to return one generated response. A mapping scheme similar to the previous Chinese subtasks were used to form 3-point relevance levels. As for the evaluation measures, the relevance scores (L2, L1, L0) = (2, 1, 0) of the returned responses were simply summed or averaged across the test topics.

WWW (NTCIR-13 and -14) and CENTRE (NTCIR-14)
The NTCIR-13 We Want Web (WWW) Task (Luo et al. 2017) was an adhoc web search task. For the Chinese subtask, three assessors independently judged each pooled web page on a 4-point scale: (3, 2, 1, 0); the scores were then summed up to form the final 10-point relevance levels. For the English subtask, two assessors independently judged each pooled web page on a different 4-point scale: highly relevant (2 points), relevant (1 point), nonrelevant (0 points), and error (0 points); the scores were then summed up to form the final 5-point relevance levels. In both subtasks, linear gain value settings were used to compute (Microsoft) nDCG, Q (the cutoff version (Sakai 2014)), and nERR. The NTCIR-14 WWW Task (Mao et al. 2019) was similar to its predecessor. The Chinese subtask used the following judgment criteria: highly relevant (3 points), relevant (2 points), marginally relevant (1 point), nonrelevant (0 points), garbled (0 points). Although three assessors judged each topic, the final relevance levels were obtained on a majority-vote basis rather than taking the sum; hence 4-point scale relevance levels were used this time. As for the English subtask, 5-point relevance levels were obtained by following the methodology of the NTCIR-13 English subtask. Both subtasks adhered to Microsoft nDCG, (cutoff-based) Q, and nERR with linear gain value settings.
The NTCIR-14 CLEF NTCIR TREC Reproducibility (CENTRE) task ) encouraged participants to replicate a pair of runs from the NTCIR-13 WWW English subtask and to reproduce a pair of runs from the TREC 2013 Web Track adhoc task (Collins-Thompson et al. 2014). Additional relevance assessments were conducted on top of the official NTCIR-13 WWW English test collection, by following the relevance assessment methodology of the WWW subtask. As for the evaluation of the TREC runs with the TREC 2013 Web Track adhoc test collection, the original 6-point scale relevance levels Navigational, Key, Highly relevant, Relevant, Nonrelevant, Junk were mapped to L4, L3, L2, L1, L0, L0, respectively. All runs involved in the CENTRE task were evaluated using Microsoft nDCG, (cutoff-based) Q, and nERR, with linear gain value settings.

AKG (NTCIR-13)
The NTCIR-13 Actionable Knowledge Graph (AKG) task (Blanco et al. 2017) had two subtasks: Action Mining (AM) and Actionable Knowledge Graph Generation (AKGG). Both of them involved graded relevance assessments and graded relevance measures. The AM subtask required systems to rank actions for a given entity type and an entity instance: for example, given "Product" and "Final Fantasy VIII," the ranked actions could contain "play on Android," "buy new weapons," etc. Two sets of relevance assessments were collected by means of crowd sourcing: the first set judged the verb parts of the actions ("play," "buy," etc.) whereas the second set judged the entire actions (verb plus modifier as exemplified above). Both sets of judgements were done based on 4-point relevance levels. The AKGG subtask required participants to rank entity properties: for example, given a quadruple (Query, Entity, Entity Types, Action) = ("request funding," "funding," "thing, action," "request funding"), systems might return "Agent," "ServiceType," "Result," etc. Relevance assessments were conducted by crowd workers on a 5-point scale. Both subtasks used nDCG and nERR for the evaluation; linear gain value settings were used. 17

OpenLiveQ (NTCIR-13 and -14)
The NTCIR-13 OpenLiveQ task (Kato et al. 2017) required participants to rank Yahoo! Chiebukuro questions for a given query, and the offline evaluation part of this task involved ranked list evaluation with graded relevance. Five crowd workers independently judged a list of questions for query q under the following instructions: "Suppose you input q and received a set of questions as shown below. Please select all the questions that you would want to click." Thus, while the judgement is binary for each assessor, 6-point relevance levels were obtained based on the number of votes. (Microsoft) nDCG, Q, and ERR were computed using a linear gain value setting.
The NTCIR-14 OpenLiveQ-2 task ) is similar to its predecessor, but this time the evaluation involved unjudged documents, as the relevance assessments from NTCIR-13 were reused but the target questions to be ranked were not identical to the NTCIR-13 version. The organisers therefore used condensedlist (Sakai 2014) versions of Q, (Microsoft) nDCG, and ERR. Also, for OpenLiveQ-2, the organisers switched their primary measure from nDCG to Q, as Q substantially outperformed nDCG (at l = 5, 10, 20) in terms of correlation with online (i.e., clickbased) evaluation in their experiments (Kato et al. 2018). It can be observed that (a) the majority of the past NTCIR ranked retrieval tasks utilised graded relevance measures; and that (b) even a few relatively recent tasks, namely, SpokenQuery& Doc and MathIR from NTCIR-12 held in 2016, refrained from using graded relevance measures. As was discussed in Sect. 1.2.1, researchers should be aware that binary relevance measures with different relevance thresholds (e.g., Relaxed AP and Rigid AP) cannot serve as substitutes for good graded relevance measures. If the optimal ranked output for a task is defined as one that sorts all relevant documents in decreasing order of relevance levels, then by definition, graded relevance measures should be used to evaluate and optimise the retrieval systems.

Summary
One additional remark regarding Tables 1.1 and 1.2 is that the NTCIR-5 CLIR overview paper (Kishida et al. 2007) was the last to report on RP curves; the RP curves completely disappeared from the NTCIR overviews after that. This may be because (a) interpolated precisions at different recall points (Sakai 2014) do not directly reflect user experience; and (b) graded relevance measures have become more popular than before.
Over the past decade or so, some researchers have pointed out a few disadvantages of using graded relevance, especially in the context of promoting preference judgements (e.g., Bashir et al. 2013;Carterette et al. 2008). Carterette et al. (2008) argue that (i) it is difficult to determine relevance grades in advance and to anticipate how the decision will affect evaluation; and (ii) having more grades means more burden on the users. Regarding (i), while it is important to always check how our use of grades affects the evaluation outcome, in many cases relevance grades can be naturally defined based on individual assessors' labels; I argue that it is useful to preserve the raw judgements in the form of graded relevance rather than to collapse them to binary; see also the discussion below on label distributions. Regarding (ii), rich relevance grades can be obtained even if the individual judgements are binary or tertiary, as I have illustrated in this chapter. Moreover, while I agree that simple side-by-side preference judgements are useful (and can even be used for constructing graded relevance data), it should be pointed out that some of the approaches in the preference judgements domain require more complex judgement protocols than this, e.g., graded preference judgements (Carterette et al. 2008), and contextual preference judgements (Chandar and Carterette 2013;Golbus et al. 2014). Moreover, while I agree that utilising preference judgements is a promising avenue for future research, the incompleteness problem of preference judgements needs to be solved. What lies beyond graded relevance then? Here is my personal view concerning offline evaluation (as opposed to online evaluation using click data etc.). Information Retrieval (IR) and Information Access (IA) tasks have diversified, and relevance assessments require more subjective and diverse views than before. We are no longer just talking about whether a scientific article is relevant to the researcher's question (as in Cranfield); we are also talking about whether a response of a chatbot is "relevant" response to the user's utterance, about whether a reply to a post on social media is "relevant," and so on. Graded relevance implies that there should be a single label for each item to be retrieved (e.g., "this document is highly relevant"), but these new tasks may require a distribution of labels reflecting different users's points of view. Hence, instead of collapsing this distribution to form a single label, methods to preserve the distribution of labels in the test collection may be useful, as was implemented at the Dialogue Breakdown Detection Challenge ). The Dialogue Quality (DQ) and Nugget Detection (ND) subtasks of the NTCIR-14 STC task were the very first of NTCIR efforts in that direction: they compared gold label distributions with systems' estimated distributions (Sakai 2018;Zeng et al. 2019). See also Maddalena et al. (2017) for a related idea.
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